This is not the complete question, the complete question is:
Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports X, the claim amount divided by 1000. Actuary B reports Y, which is X rounded to the nearest integer from 0 to 10.Calculate the absolute value of the difference between the 4th moment of X and the 4th moment of Y
A) 0
B) 33
C) 296
D) 303
E) 533
Answer: B) 33
Step-by-step explanation:
First lets say;
z: automobile claim amounts
x: the claim amount dived by 1000
y: x rounded to the nearest integer from 0 to 10
z ≅ V[0, 10,000]
x = z / 1000 ≅ V[0, 10 ] ⇒ Fx { 1/10, 0 ≤ x ≤ 10} 0, 0/10
y = {0, 0 ≤ x < 0.5
1, 0.5 ≤ x < 1.5
2, 1.5 ≤ x < 2.5
3, 2.5 ≤ x < 3.5
↓
9, 8.5 ≤ x < 9.5
10, 9.5 ≤ x < 10
SO 4th moment of x = E(x²) = ∫₀¹⁰x⁴ 1/10 dₓ
= 1/10 (x⁵ / 5)₀¹⁰
= 10⁵ / (10 * 5)
= 100000/50
= 2000
Now
4th moment of y = E(y⁴) = ∑/y y⁴ p( y=y)
= 0⁴p( y=0) + 1⁴p( y=1 ) + 2⁴p( y=2) + → + 10⁴p( y=10)
= 0 + 1⁴.p( 0.5 ≤ x < 1.5) + 2⁴.p( 1.5 ≤ x < 2.5) + 3⁴.p( 2.5 ≤ x < 3.5 ) + → + 10⁴.p( 9.5 ≤ x < 10 )
= 1/10 [ 1⁴(1.5 - 0.5) + 2⁴(2.5 - 1.5) + → + 9⁴(9.5 - 8.5) + 10⁴(10 - 9.5)]
= 1/10 [ 1⁴ + 2⁴ + → + 9⁴ + 1/2*10⁴] = 2033.3
now the absolute difference will be
AD = ║E(x⁴) - E(y⁴)║
= ║ 2000 - 2033.3║
= 33.3 ≈ 33
PLZ HELP PLZ
I WOULD APPRECIATE IT PLZ
19 and 20
let given points be
(x1,y1)=(-3,-3)
and(x2,y2)=(3,1)
equation of given line ,
(y-y1)= ((y2-y1)/(x2-x1))×(x-x1)
therefore, 2x-3y+3=0.........(i)
comparing (i ) with ax+by+c=0 we get
a=2
b= -3
c=3
then the line parallel to (i) is
ax+by+k=0 where k = -bc
that is, 2x-3y+9=0 is the required equation
Answer:
19. y = 2/3x - 10/3
20. y = -3/2x - 4
Step-by-step explanation:
First off, we need to find the equation of the line shown. There are two coordinates given. The slope of the line is (1 - -3) / (3 - -3) = 4 / 6 = 2/3. The line obviously intersects the y-axis at -1, so the equation of the line is y = 2/3x - 1.
19. If a line were to be parallel to the given line, the line would have to have a slope of 2/3. So, we have y = 2/3x + b.
To solve for b, all you need to do is substitute the coordinates given, (2, -2), and solve.
-2 = (2/3) * 2 + b
b + 4/3 = -2
b = -6/3 - 4/3
b = -10/3.
So, the equation of the line is y = 2/3x - 10/3.
20. If a line were to be perpendicular to the given line, the line would have a slope that is the negative reciprocal of the given line's slope. The slope would be -3/2. So, we have y = -3/2x + b.
To solve for b, once again, put in the given coordinates, (-4, 2), and solve.
2 = (-3/2) * (-4) + b
b + 6 = 2
b = -4
So, the equation of the line is y = -3/2x - 4.
Hope this helps!
This recipe makes 6 portions of potato soup. Richard follows the recipe but wants to make 18 portions. Complete the amounts of each ingredient that he needs. Recipe: Serves 6 60 ml oil 80 g onions 450 g potatoes 600 ml milk
Answer:
1080 ml oil
240 g onions
1350 g potatoes
1800 ml milk
Step-by-step explanation:
18 ÷ 6 = 3
every ingredient x 3
60 x 6 = 360 , 360 x 3 = 1080 ml oil
80 x 3 = 240 g onions
450 x 3 = 1350 g potatoes
600 x 3 = 1800 ml milk
What is the value of x?
Answer:
68 Degrees
Step-by-step explanation:
A triangle is 180 degrees. So,
Add 75 + 37 = 112
Subtract 112 from 180 = 68
Answer: 68°
Step-by-step explanation: To find the missing angle measure, represented by x, it's important to understand that the sum of the measures of the angles of a triangle is 180°
So to find the value of x, we can
setup the equation x + 75° + 37° = 180°.
Solving from here, we first simplify the left side of the equation.
So 75 + 37 is 112 and we have x + 112° = 180°
Next, to get x by itself, we subtract 112° from both sides.
On the left, the 112's cancel out and we are left with x.
On the right, 180° - 112° is 68°.
So x = 68°.
This means that the missing angle
measure in the triangle shown is 68°.
HELP ME PLEASE PLEASE
Answer:
x=0 , y=4
Step-by-step explanation:
3x - 3y = -12 - eq1
4x + 3y = 12 - eq 2
Add eq 1 and 2
3x - 3y + 4x +3y = -12 + 12
7x = 0
x = 0
By substituting the value of x in eq 2
4x + 3y = 12
4(0) + 3y = 12
3y = 12
y = 12 / 3
y = 4
Answer:
(x,y)=(24,-28)
Step-by-step explanation:
1. Multiply both sides by -1
3x+3y=-12
-4x-3y-=-12
2. Elimnate one variable by adding the equations
-x=-24
3. Change the signs
x=24
4. Susbstitue the value of x in the equation 3x+3y=-12
3 x 24 + 3 y = -12
y=-28
5. Check the solution by plugging in the values.
(x,y)=(24,-28)
HELP ME PLZ!!!!!!!! Brainliest will be given, THANK YOU!!!!
Answer:
Step-by-step explanation:
5*2=10, 10*2=20...
it is a geometric progression with ratio= 2
a11=a10*2=2560* 2=5120
Evaluate 3|−5| − 2|−2|. Question 22 options: −11 −19 11 19
Answer:
11
Step-by-step explanation:
3|−5| − 2|−2|
Absolute value means take the non-negative value
3 * 5 -2 * 2
15 - 4
11
A conical-shaped umbrella has a radius of 0.4 m and a height of 0.45 m. Calculate the amount of fabric needed to manufacture this umbrella. (Hint: an umbrella will have no base)
Answer:
The correct answer will be "0.756596 m²".
Step-by-step explanation:
The given values are:
The radius of an umbrella,
r = 0.4 m
The height of an umbrella,
h = 0.45 m
As we know,
The lateral surface of an umbrella will be:
⇒ [tex]\pi r\sqrt{r^2+h^2}[/tex]
On substituting the values, we get
⇒ [tex]\pi \times 0.4\sqrt{(0.4)^2=(0.45)^2}[/tex]
⇒ [tex]0.756596 \ m^2[/tex]
So that the amount of fabric needed will be "0.756596 m²".
in a box of chocolates, 1/5 of the chocolates contains nuts. the rest do not.
write down the ratio of the number of chocolates that contains nuts to the number of chocolates that do not contain nuts .
give you answer in the form 1: n
Answer:
the ratio would be 1:4
Step-by-step explanation:
ratio of those who has nuts:
1/5
ratio of those who dont:
1-1/5=4/5
one against another:
1/5 : 4/5 = 1:4 = with : without
Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the value of x in the image below.
Answer:
16
Step-by-step explanation:
64 = 4x
64/4 = 4x/4
16 = x
On piece of paper, graph f(x) =5• (0.4)^x
Answer:
When we use a graphing calc, we should see that we get A as our best choice.
Step-by-step explanation:
Two students have devised a dice game named “Sums” for their statistics class. The game consists of choosing to play odds or evens. Roll 2 3 4 5 6 7 8 9 10 11 12 P(roll) StartFraction 1 Over 36 EndFraction StartFraction 2 Over 36 EndFraction StartFraction 3 Over 36 EndFraction StartFraction 4 Over 36 EndFraction StartFraction 5 Over 36 EndFraction StartFraction 6 Over 36 EndFraction StartFraction 5 Over 36 EndFraction StartFraction 4 Over 36 EndFraction StartFraction 3 Over 36 EndFraction StartFraction 2 Over 36 EndFraction StartFraction 1 Over 36 EndFraction Each person takes turns rolling two dice. If the sum is odd, the person playing odds gets points equal to the sum of the roll. If the sum is even, the person playing evens gets points equal to the sum of the roll. Note that the points earned is independent of who is rolling the dice. If Jessica is challenged to a game of Sums, which statement below is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens? E(evens) will be more because there are more even numbers that result from rolling two dice. Therefore, Jessica should play evens. E(odds) will be more because the probability for each odd number being rolled is greater. Therefore, Jessica should play odds. E(evens) will be more because the value of the even numbers on the dice are more. Therefore, Jessica should play evens. E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Answer:
(D)E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Step-by-step explanation:
The table of the probability of rolling the sums is presented below.
[tex]\left\begin{array}{ccccccccccccc}$Roll&2&3&4&5&6&7&8&9&10&11&12\\\\$Prob&\frac{1}{36}&\frac{2}{36}&\frac{3}{36}&\frac{4}{36}&\frac{5}{36}&\frac{6}{36}&\frac{5}{36}&\frac{4}{36}&\frac{3}{36}&\frac{2}{36}&\frac{1}{36} \end{array}\right[/tex]
P(an even sum)
[tex]=\frac{1}{36}+\frac{3}{36}+\frac{5}{36}+\frac{5}{36}+\frac{3}{36}+\frac{1}{36} \\\\=\frac{18}{36}[/tex]
Therefore, P(an odd sum) [tex]=\frac{18}{36}[/tex]
Therefore, E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Answer:
D /Even-odds
Step-by-step explanation:
just took test on edge 2020
a bonus of 4200 is shared by 10 people who works for a company.40% of the bonus is shared equally between 3 managers the rest of the bonus is shared equally between 7 sales people.Peter, one of the sales people says," if the bonus is shared equally between 10 people i will get 25% more money. Janet a manager, says," no you wont get that much extra. show that Janet is correct by working out how much peter thinks he would get and how much he would actually get.
Step-by-step explanation:
if each the bonus is shared equally each will get 420
if 40% is shared by managers each manager will get 560
if 7 sales persons share 60% each will get 360
therefore Peter salesperson will get 360
but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct
The question is in the picture attached
Answer:
≈ 10.7 ft
Step-by-step explanation:
We have 2 secants to a circle from an external point.
The product of the measure of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.
let the internal part of the right secant be x , then
6(6 + x) = 4(4 + 12) = 4 × 16 = 64 ( divide both sides by 6 )
6 + x ≈ 10.7 ( subtract 6 from both sides )
x ≈ 4.7
length of pass = 6 + 4.7 = 10.7
What are the factors of the function represented by this graph?
710
+6
+
+2
-10
-6
8
8
10
-2
4
-6
-8
+-10
A
(x-4) and (x-8)
B
(x-4) and (x+8)
C.
(x+4) and (x-8)
(x + 4) and (x+8)
Answer:
C. (x+4) (x-8)
Step-by-step explanation:
Take the graph for example both x values are -4 & positive 8
Complete the solution of the equation. Find th
value of y when x equals -4.
- 8x + y = 37
Enter the correct answer.
Answer:
64
Step-by-step explanation:
Find the least common multiple of x2 + 4x + 3 and x2 + 7x + 12.
Answer:
( x+1) (x+3) (x+4)
Pls, help. Trigonometry. Please answer in short sentences I'm not picking. Please answer a-i.
Answer:
a . See attachment
b. because we will find the distance from the bottom of the ladder to the base of the building.
c. sin 60 = opposite side / hypotenuse
d.sin 60 = x / 10
e . 8.66 ft =x
f. see attachment
i. cos 60° = adjacent side / hypotenuse
Step-by-step explanation:
a . See attachment
b. because cos 60° = adjacent side / hypotenuse, the hypotenuse is equal to the length of the ladder (10), and the adjacent side that we will find is the distance from the bottom of the ladder to the base of the building. not the height that the ladder reaches .
c. sin 60 = opposite side / hypotenuse
Because we will find the opposite side which is the height that the ladder reaches.
d.sin 60 = x / 10
e .
0.866025403 = x/10
10 (0.866025403) =x
8.66 ft =x
f. see attachment
i. cos 60° = adjacent side / hypotenuse
Because we will find the adjacent side which is the distance from the bottom of the ladder to the base of the building.
PLEASE HELP ASAP THANKS A LOT
Answer:
The 8ft tall pine tree will not affect the box plot here is why........
Outliers are important because they are numbers that are "outside" of the Box Plot's upper and lower fence, though they don't affect or change any other numbers in the Box Plot they are still important.
If you want to find your fences you will first take your IQR and multiply it by 1.5. I call this your "magic number".
Lower fence: Take your Q1 and subtract it from your magic number, that number your get is your lower fence.
Upper fence: Take your Q3 and add it to your magic number, that number you get is your upper fence.
Evaluate: [tex]3-2^2+4*3+5[/tex]
Answer:
16
Step-by-step explanation:
Apply PEMDAS:
Solve the exponent, multiply from left to right, and then subtract and add from left to right.
[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]
Answer: 16
Step-by-step explanation:
The important thing to remember here is the Order of Operations
The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.
There are no parentheses.
Exponents: 3 - 4+4*3+5
Multiplication and Division: 3 - 4 + 12 + 5
Addition and Subtraction:
-1+12+5
11+5
16
Hope it helps <3
Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (2,3) A. (-2, -3) B. (3, -2) C. (2, -3) D. (-3, 2)
Answer:
D
Step-by-step explanation:
Given
[tex]R_{y-axis}[/tex] ￮ [tex]R_{y=x}[/tex] : (2, 3 )
Then the order of reflections is from right to left, that is
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , thus
(2, 3 ) → (3, 2 )
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , thus
(3, 2 ) → (- 3, 2 ) → D
A square with side length c has an area of 81 square centimeters. The following equation shows the area of the square. c^2 = 81. What is the side length of the square in centimeters?
Answer:
9 cm
Step-by-step explanation:
c^2=81
Take the square root of both sides.
The square root of c^2 is c.
The square root of 81 is 9.
c=9
Answer:
C = 9 centimeters
Step-by-step explanation:
First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 * 9 = 81. Thus the answer is 9 centimeters.
Solve using derivatives.
I have no clue where to start on this I really need help please.
Please show steps and diagram.
Answer:
Below in bold.
Step-by-step explanation:
The surface area of the box
= x^2 + 4hx where x = a side of the square base and h is the height.
So x^2 + 4hx = 8
The volume of the box
V = x^2h
From the first equation we solve for h
4hx = 8 - x^2
h = (8 - x^2) / 4x
Now we substitute for h in the formula for the volume:
V = x^2 * (8 - x^2) / 4x
V = 8x^2 - x^4 / 4x
V = 2x - 0.25x^3
Finding the derivative:
V' = 2 - 0.75x^2 = 0 for max/mimn values
x^2 = 2/ 0.75 = 2.667
x = 1.633.
So the length and width of the base is 1.633 m and the height
= ( 8 - 2.667) / (4*1.633)
= 0.816 m
The maximum volume = 0.816 * 2.667 = 2.177 m^2.
The answers are correct to the nearest thousandth.
PLEASE HELP
Compare the functions show below:
Which function has the most x-intercepts?
A) f(x)
B) g(x)
C) h(x)
D) all three functions have the same number of x-intercepts.
Answer:
A) f(x)
Step-by-step explanation:
f(x) has 4 x-intercepts, becoz it "cross" the x axis 4 times.
g(x) would have an infinite number of intercepts coz it is a cos function, but it gave a limit to the domain which is 0 to 2[tex]\pi[/tex], so it only has 2 x-intercepts.
h(x) is the degree of x^3, so in theory, it has 3 x-intercepts.
The function that has the most x-intercept is given by: Option A: f(x)
What is x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.
The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 becuase at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
What is the maximum number of roots a polynomial equation can have?Suppose that we've got a polynomial function as y = p(x),
where p(x) is of degree n (the highest power its variable pertains in any of its composing terms).
Then, the maximum number of roots it can possess for p(x) = c (c is a constant), or p(x) - c = 0 is n
So, the number of roots of p(x) - c = 0 cannot exceed the degree of p(x).
From the graph, we see that:
f(x) intersects x-axis at 4 places, so it has 4 x-intercepts.
g(x) intersects the x-axis at 2 places as in the graph, and therefore, it has 2 x-intercepts.
h(x) is a polynomial of degree 3. The maximum number of intercepts it can have is the maximum number of roots h(x) = 0 can have which is 3(the degree of h(x) ). So it cannot be bigger than 3.
Thus, the function that has the most x-intercept is given by: Option A: f(x)
Learn more about x-intercept here:
https://brainly.com/question/14764115
This system of equations is shown on the graph: 2y − 4x = 6 y = 2x + 3 Which statement about the system is true?
Answer:
The system has infinity many solutions
Step-by-step explanation:
If it had no solutions there would be another like that does not go through it....if it was one solution it would have another like going through the other line....and since it has two lines that are on top of each other in the same point it's infinity solutions
Answer:
likely Option: DStep-by-step explanation:
Expand the following:
a) x(x + 2)
b) x(2x - 5)
c) 2x(3x + 4)
d) 6x(x - 2)
Answer:
[tex]a. \: {x}^{2} + 2[/tex] [tex]b. \: 2 {x}^{2} - 5x[/tex] [tex]c. \: 6 {x}^{2} + 8x[/tex] [tex]d. \: 6 {x}^{2} - 12x[/tex]solution,
[tex]a. \: x(x + 2) \\ \: \: = x \times x + 2 \times x \\ \: \: = {x}^{2} + 2x[/tex]
[tex]b . \: x(2x - 5) \\ \: = x \times 2x - x \times 5 \\ \: \: = 2 {x}^{2} - 5x[/tex]
[tex]c. \: 2x(3x + 4) \\ \: = 2x \times 3x + 2x \times 4 \\ \: \: = 6 {x}^{2} + 8x[/tex]
[tex]d. \: 6x(x - 2) \\ \: \: = 6x \times x - 6x \times 2 \\ \: \: = 6 {x}^{2} - 12x[/tex]
Hope this helps...
Good luck on your assignment..
What is the quotient? StartFraction a minus 3 Over 7 EndFraction divided by StartFraction 3 minus a Over 21 EndFraction StartFraction negative (a minus 3) squared Over 147 EndFraction StartFraction (a minus 3) squared Over 147 EndFraction 3 –3
Answer:
Correct answer is
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Step-by-step explanation:
Let us rephrase the given statement mathematically.
We are given the fractions as:
[tex]\dfrac{a-3}{7}[/tex]
to be divided by:
[tex]\dfrac{3-a}{21}[/tex]
To find:
[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]
Now, let us have a look at the division rule in fractions:
[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]
is equivalent to
[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]
In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]
Now solving the given fraction by applying above rules:
[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]
[tex]\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3[/tex]
So, correct answer is:
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Answer:
d on edg
Step-by-step explanation:
taking test rn
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 100 degrees and the low temperature of 70 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. Assume the next low is 24 hours later.
Answer:
The function for the outside temperature is represented by [tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex], where t is measured in hours.
Step-by-step explanation:
Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:
Amplitude
[tex]A = \frac{100\º-70\º}{2}[/tex]
[tex]A = 15\º[/tex]
Mean temperature
[tex]\bar T = \frac{70\º+100\º}{2}[/tex]
[tex]\bar T = 85\º[/tex]
Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:
[tex]T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right][/tex]
Where:
[tex]\bar T[/tex] - Mean temperature, measured in degrees.
[tex]A[/tex] - Amplitude, measured in degrees.
[tex]\tau[/tex] - Daily period, measured in hours.
[tex]t[/tex] - Time, measured in hours. (where t = 0 corresponds with 5 AM).
If [tex]\bar T = 85\º[/tex], [tex]A = 15\º[/tex] and [tex]\tau = 24\,h[/tex], the resulting function for the outside temperature is:
[tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex]
PLEASE HELP
Choose the correct conic section to fit the equation.
X^2/16-y^2/4=1
1.Circle
2.Ellipse
3. Parabola
4. Hyperbola
Answer:
2.Ellipse
Step-by-step explanation:
The given equation represents an ellipse.
Standard form of ellipse is given as:
[tex] \frac{x^2}{a^2} +\frac{y^2}{b^2} = 1\\\\
\implies \frac{x^2}{16} - \frac{y^2}{4} = 1\\[/tex]
2. The price of a gallon of milk has been rising about 1.36% per year since 2000. a. What type of function would be best to model this scenario? Choose one of the types of functions studied in this course. Explain why you chose this answer. b. Write a formula for the function you chose to model this scenario. What does the independent variable in your function represent? c. If milk costs $4.70 now, what will it cost next year? Show how you found the answer. d. If milk costs $4.70 now, how long will it take for the price to top $5? Show how you found the answer.
Answer:
(a)Exponential
(b)[tex]P(t)=4.70(1.0136)^t[/tex]
(c)The price of milk next year will be: $4.76
(d)5 years
Step-by-step explanation:
The price of a gallon of milk has been rising about 1.36% per year since 2000.
(a)Since the price grows by a percentage (or constant factor) each year, an exponential function would be best to model the scenario.
(b)The exponential growth model is given as:
[tex]P(t)=P_0(1+r)^t$ where:\\P_0$=Initial Price\\r=Growth factor\\t=time (in years, for this case)[/tex]
The independent variable in the function is t. This represents the number of years since 2000.
(c)
[tex]I$nitial Price, P_0=\$4.70\\r=1.36\%=0.0136\\P(t)=4.70(1+0.0136)^t\\\\P(t)=4.70(1.0136)^t[/tex]
Therefore, the price of milk next year will be:
[tex]P(1)=4.70(1.0136)^1=\$4.76[/tex]
(d)We want to determine how long it will take for the price to top $5.
P(t)=$5
[tex]5=4.70(1.0136)^t\\$Divide both sides by 4.7$\\(1.0136)^t=\frac{5}{4.7} \\$Change to logarithm form\\t=Log_{1.0136}\frac{5}{4.7}\\t=4.58[/tex]
Therefore, in exactly 4.58 years, the milk price would be $5. Therefore, by the 5th year, the milk price would top $5.
Can someone help me out with these math questions?
You can pick one to answer or chose to answer both!
I’d appreciate the help thank you!