NO LINKS!! Based on each graph below, find the equation of the exponential function y= ab^x
Answers
Answer:
[tex]\textsf{a)} \quad y=3\left(\dfrac{5}{3}\right)^x[/tex]
[tex]\textsf{b)} \quad y=40\left(\dfrac{1}{3}\right)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question (a)From inspection of the diagram, two points on the graph are:
(0, 3)(1, 5)The y-intercept is the y-value when x = 0.
As a is the y-intercept, and the y-intercept is 3:
[tex]\implies y=3 \cdot b^x[/tex]
Substitute point (1, 5) into the equation and solve for b:
[tex]\begin{aligned}(1,5) \implies 5&=3 \cdot b^1\\5&=3b\\b&=\dfrac{5}{3}\end{aligned}[/tex]
Therefore, the equation of the exponential function is:
[tex]y=3\left(\dfrac{5}{3}\right)^x[/tex]
Question (b)From inspection of the diagram, two points on the graph are:
(0, 40)(-1, 120)The y-intercept is the y-value when x = 0.
As a is the y-intercept, and the y-intercept is 40:
[tex]\implies y=40 \cdot b^x[/tex]
Substitute point (-1, 120) into the equation and solve for b:
[tex]\begin{aligned}(-1,120) \implies 120&=40 \cdot b^{-1}\\\dfrac{120}{40}&=\dfrac{1}{b}\\b&=\dfrac{40}{120}\\ b&=\dfrac{1}{3}\end{aligned}[/tex]
Therefore, the equation of the exponential function is:
[tex]y=40\left(\dfrac{1}{3}\right)^x[/tex]
Related Questions
Will give brainliest
50 points
Answers
Answer: D
Step-by-step explanation:
The parent function abs(x) is a V, similar to graph B.
When it is multiplied by a negative number then it reflects across the Y axis, and if the number is greater than 1, then the graph is horizontally compressed (like you're squishing the sides together, closer to each other). If the number is less than 1, either decimals or a fraction, then it is stretched (like you are pulling the sides away from each other and they are getting wider).
In this case you are multiplying abs(x) by 4, which is greater than 1 so it is compressed by a factor of 4, and then multiplying it by a negative, which reflects it across the y axis.
The equation of line u is y–3=7(x–5). Parallel to line u is line v, which passes through the point (1,9). What is the equation of line v?
Answers
Answer:
y - 9 = 7(x - 1)
Step-by-step explanation:
The given equation is in Point Slope Form: y - y₁ = m(x - x₁)
m is the slope, and parallel lines have the same slope (7)
x₁ and y₁ are the coordinates of a point on the line
Your redecorating your bedroom, and you want to put in a dressing table. The wall where you want to put it measures 4.7m. There is also a cupboard door on this wall, which takes up 410mm. The dressing table you like is 123cm wide. Once you've bought the dressing table , how much space on the wall, do you have left, not including the cupboard doors? I need this working out in metres please.
Answers
Answer:
3.06 meters
Step-by-step explanation:
The first thing you want to do, since we are working with different units here, is find out how many centimeters make a meter... and so on.
1cm = 0.01m
1mm = 0.001m
123cm = 1.23m (Dressing table)
410mm = 0.41m (Cupboard door)
Now all we need to do is subtract.
We can add the two numbers together or (If you prefer) subtract separately.
1.23 + 0.41 = 1.64
Now subtract that number from the measurement of the wall:
4.7 - 1.64 = 3.06
The amount of space left is 3.06m.
Is the sum of 3.04 and √20 rational or irrational? Explain.
Answers
Answer:
Irrational
Step-by-step explanation:
A rational number can be expressed as p/q where p and q are integers
3.04 is rational since it can be expressed as 304/100
√20 is not rational. √20 = √(4·5) = √4·√5 = 2√5
While 2 is a rational number, √5 is irrational since 5 is a prime number and square roots of primes are not rational
An irrational number multiplied by a rational number is irrational so √20 is irrational
An irrational number added to a rational number results in an irrational number.
So 3.04 + √20 is irrational
The radius of a cone is 2.5 units. The volume of the cone is 19 cubic units
Answers
The formula for the volume of a cone is given by the following equation:
V = 1/3 * π * r2 * h
where V is the volume of the cone, r is the radius of the cone, and h is the height of the cone.
In this case, we are given that the radius of the cone is 2.5 units and the volume of the cone is 19 cubic units. We can use this information to complete the expression that represents the height of the cone as follows:
V = 1/3 * π * r2 * h
19 cubic units = 1/3 * π * 2.5 units2 * h
19 cubic units = 1/3 * π * 6.25 units2 * h
19 cubic units = 1/3 * 19.63 units2 * h
19 cubic units = 6.54 units2 * h
h = 19 cubic units / 6.54 units2
h = 2.9 cubic units / 6.54 units
Therefore, the expression that represents the height of the cone is 2.9 cubic units / 6.54 units.
The perimeter of a triangle is 58 cm. The triangle is isosceles, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, then it would be equilateral. Find the base of the original
triangle.
A. 12 cm
B. 11 cm
C. 23 cm
D. 16 cm
Answers
The base of the original triangle is 12 centimetres.
How to find the base of the original triangle?A triangle is a polygon with three sides. The perimeter of a triangle is 58 cm. The triangle is isosceles.
An isosceles triangle is a triangle with 2 sides equal to each other and two angles equal to each other.
Therefore, let's find the base of the original triangle when the base were lengthened by 4 cm and each leg were shortened by 7 cm,
Hence,
let
x = length of legs
y = length of the base
Therefore,
2x + y = 58
Hence,
y + 4 = x - 7
x - y = 11
2x + y = 58
x - y = 11
3x = 69
x = 69 / 3
x = 23
-y = 11 - 23
-y = -12
y = 12
Therefore,
base of the original triangle = 12 cm
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You are a construction worker who is laying down concrete drainage pipes. Each pipe is 5 feet long and 3 inches thick, and has an outside diameter of 6.5 feet. You lay down 4 drainage pipes end to end.
At any given time, what is the volume of water that passes through the 4 drainage pipes at half capacity? Round the answer to the nearest tenth of a cubic foot.
141.3
165.8
282.6
306.6
565.2
Answers
Answer:
Volume = 282.6 ft.²
Step-by-step explanation:
Volume: V = πr²h
Step 1: The answer needs to be in cubic feet, so convert all units to feet
1. 3 ft./12 in. = 0.25 ft.
Step 2: Subtract 0.5 ft from 6.5 ft to find the actual diameter of the pipe that the water will be passing through
2. 6.5 ft. - 0.5 ft. = 6 ft.
Step 3: Plug 3 ft. (radius), 3.14 for π, and 5 ft for h
3. V = (3.14)(3 ft.)²(5 ft.)
Step 4: Solve for the V (volume)
4. V = (3.14)(9 ft.)(5 ft.) → V = (28.26)(5) → V = (28.26)(5) → V = 141.3 ft.²
Step 5: Divide 141.3 by 2, since we want half the capacity
5. 141.3 ft.²/2 = 70.65 ft.²
Step 6: Multiply 70.65 by 4 since we want the total volume of water passing through four pipes
6. 70.65 ft.² ∙ 4 = 282.6 ft.²
Graph the equation.
y
=
−
4
(
x
+
2
)
2
−
1
y=−4(x+2)
2
−
Answers
Answer:
see instructions
Step-by-step explanation:
1. (x + 2) = 0 gives us x = -2 = x coordinate of vertex; and
the -1 at the end gives us the y coordinate.
Move the vertex of the parabola to the point (-2,-1)
2. The -4 in front of the (x+2)² gives the direction and stretch of the parabola. FROM the Vertex, position the other point Down 4 and Right 1 (at (1,-5)).
The variables a, b, c, and d are graphed on the number line shown.
Use the number you answer the questions in the chart
Answers
The correct values are;
⇒ a - d = - 2
⇒ c - a = 7
⇒ b - c = - 8
⇒ d - c = - 5
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
The number line is shown in figure.
The values are,
a = - 3
b = - 4
c = 4
d = - 1
Now,
All the values are find as;
⇒ a - d = - 3 - (- 1)
= - 3 + 1
= - 2
⇒ c - a = 4 - (-3)
= 4 + 3
= 7
⇒ b - c = - 4 - 4
= - 8
⇒ d - c = - 1 - 4
= - 5
Thus, The correct values are;
⇒ a - d = - 2
⇒ c - a = 7
⇒ b - c = - 8
⇒ d - c = - 5
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Jackson’s motorcycle gets 28 kilometers per liter. He drives 336 kilometers and gas is $1.43 per liter. Complete parts (a) and (b) below.
(A) how much does the gas used for the trip cost?
-round to the nearest cent as needed-
(B) how many miles per gallon does Jackson’s motorcycle get?
-round to the nearest cent as needed-
Answers
The gas for the Trip cost is $8.39
The amount of gas motorcycle needed is 12 Liter of gas.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Jackson’s motorcycle gets 28 kilometers per liter.
He drives 336 kilometers and gas is $1.43 per liter.
The amount of gas motorcycle needed
= 336/28
= 12 Liter of gas
and, The gas for the Trip cost = 12/1.43
= $8.39
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A bakery can make 640 bagels in 4 hours how many can it make in 8 hours and 6 hours.PLEASE HURRY UP THIS IS DUE IN 10 MINUTES <3333
Answers
Hello!
What does this problem want:
how many bagels in 8 hourshow many bagels in 6 hoursWhat we need to find: rate of bagels made per hour
[tex]\text{Rate}=\frac{\text{Total number of bagels}}{\text{Number of hours}} =\frac{640}{4} =160 \text{ bagels per hour}[/tex]
Thus
how many bagels in 8 hours8 * 160 = 1280 bagels
how many bagels in 6 hours6 * 160 = 960 bagels
Hope that helps!
f(x)=1/2x+8 reflect x axis
Answers
The function of reflect x-axis is g(x) = -(1/2)*x - 8, according to the question.
What do you mean by function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
According to the given question,
First, let's define a reflection over the x-axis.
If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).
Now, when we have a function
f(x) = y, the points can be written as:
(x, y = f(x) ) = (x, f(x))
Then, after the reflection over the x-axis, we have:
(x, y = g(x)) = (x, -f(x))
So now we have g(x) = -f(x)
and we know that f(x) = (1/2)*x + 8
then our new function is g(x) = y = -f(x) = -( (1/2)*x + 8) = -(1/2)*x - 8.
g(x) = -(1/2)*x - 8.
Therefore, the required answer is g(x) = -(1/2)*x - 8.
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y=9.44x+84.182
is this function a good model for the data
Answers
Answer:
Step-by-step explanation:
443
The area of the smaller regular pentagon is about 27.5 cm².
What is the best approximation for the area of the larger regular pentagon?
11cm²
172 cm²
70 cm²
275 cm²
Answers
Answer:172 cm²
Step-by-step explanation:
when we use the formula, and we can solve out is like 172.05 and round to tenth and will have the answer
Formula is 1/2 × p × a
[3x (4.6÷2)] +14.1 =
Answers
Answer:
21
Step-by-step explanation:
PEMDAS : Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.
First, we want to deal with the parenthesis within the parenthesis.
(4.6/2) = 2.3
Rewrite it into the equation.
[3 * 2.3] + 14.1 = ?
Now, do the work in the parenthesis again.
[6.9] + 14.1 = ?
There isn't anymore parenthesis, exponents, or multiplication/division, so we move onto addition now and add both terms.
6.9 + 14.1 = 21
? = 21
The answer is 21.
Is (x + 7) a factor of f(x) = x3 − 3x2 + 2x − 8? Explain your reasoning.
Answers
X + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8 because it gives a remainder when x + 7 divides it.
What is a remainder?The remainder is the portion of the dividend that cannot be fairly divided by the divisor. After dividing whole numbers to find the quotient, the part that is left is called the remainder.
to know if x + 7 is a factor, x = -7 when substituted should give 0 as a remainder otherwise it is not a factor.
By substituting x = -7 we have
[tex](-7)^{3}[/tex] [tex]-3(-7)^{2}[/tex] +2(-7) - 8 = -343 -147 -14 - 8 which is -512
Therefore x + 7 is not a factor of the function.
In conclusion x + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8
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Answer:
What he said!
Step-by-step explanation:
If 3(x + 5) + 2 = 5, what is the value of x?
Answers
Answer:
-4
Step-by-step explanation:
3x+15+2=5
3x=-15-2+5
3x=-12
x=-12/3
x=-4
Answer:
x=-4
Step-by-step explanation:
Given:
[tex]3(x+5)+2=5[/tex]
To find:
The value of x.
Explanation:
It is given that,
[tex]3(x+5)+2=5[/tex]
That implies,
[tex]3(x+5)+2=5\\3x+15+2=5\\3x+17=5\\3x=5-17\\3x=-12\\x=-\frac{12}{3} \\x=-4[/tex]
Hence, the value of x is -4.
11. Ms. Still is ordering pizza and breadsticks for a school pizza party and has a budget of no more than
$91. An order of breadsticks, x, costs $7 and a pepperoni pizza, y, costs $13.
a. Write a linear inequality that describes the situation.
b. Graph the situation. Label the axes.
c. Is (5, 5, 4) a solution to the inequality? Does this oved pair make sense for this situation? Explain.
Answers
The inequality that represents the situation given will be
7x + 13y ≤ 91.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The inequality that represents the situation given will be 7x + 13y ≤ 91.
From the information given, Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $91, but no more and an order of breadsticks costs $7 while a pepperoni pizza costs $13.
Therefore, the inequality that represents the situation given will be
7x + 13y ≤ 91.
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solve 3x+1=-5 by graphing. then find the x- and y-intercepts
Answers
The graph of the equation is shown below
The x-intercept is -2
The y-intercept is undefined
Graph of linear equations and determining the interceptsFrom the question, we are to solve the equation by graphing and determine the x- and y-intercepts
The given equation is
3x + 1 = -5
To determine the x-intercepts, we will solve the equation
3x + 1 =-5
3x = -5 - 1
3x = -6
Divide both sides by 3
x = -2
Since, y is not defined in the equation, the y-intercept is undefined
The graph of the equation is shown below.
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Every day, Garrett's burrito stand uses 1 7/10 bags of tortillas. How many days will 8 1/2 bags of tortillas last?
Answers
Answer: 5 days.
Step-by-step explanation: To solve this problem, we first need to convert 1 7/10 bags of tortillas to a decimal number. We can do this by dividing the numerator of the fraction (7) by the denominator (10) and adding the result to the whole number (1) to get 1 + 7/10 = 1.7 bags of tortillas.
Next, we can divide the number of bags of tortillas that Garrett's burrito stand uses per day (1.7 bags) into the total number of bags of tortillas that are available (8.5 bags) to find out how many days the tortillas will last: 8.5 bags / 1.7 bags/day = 5 days
Therefore, the 8 1/2 bags of tortillas will last for 5 days.
30+ w =150 what does w equal?
Answers
30-30+w=150-30
w=120
We can substitute w=120 back into the equation to check it:
30+(120)=150
my teacher is asking what is 4 cubed and the options are [tex]3^{3}[/tex] , [tex]3^{3}[/tex] > 12 , [tex]4^{3}[/tex] , and 3-4 please help !
Answers
Adante begins to evaluate the expression 3 1/3x5 1/4using the steps below.
3 1/3 x5 1/4
(3 1/3x(5+1/4)
(3 1/(3+1/3)(1/4)
Answers
Step-by-step explanation:
Here you are the answer.
Math Please help!!!!! Linear vs Exponential
Answers
Answer:
linearadditivelycommon differenceabout 240.12Step-by-step explanation:
Given the values in the table, you want to know if they represent a linear or exponential relation, along with the common difference or ratio, as applicable.
ChangesThe first attachment shows the differences and ratios between successive table values. Neither the differences nor the ratios are constant. The wide variation in ratios and the relatively smaller variation in differences suggests the table is best modeled by a linear function.
Changes when the function is linear are additive. That is, the function values have a common difference.
Common differenceThe average difference between table values is (949.92 -229.44)/3 = 240.16. A linear regression analysis gives a slope of 240.12 as the "best fit" to the table values.
You can see from the first attachment that the differences are not constant, so there isn't really a common difference. The difference is approximately 240.12.
__
Additional comment
The second attachment shows linear and an exponential regression applied to this data. The residuals are much smaller for the linear approximation.
The slope of the line (common difference) is estimated at 240.12 using the regression formula. This makes the mean square residuals a minimum. As we show above, this slope is different (slightly lower) than the slope of the line through the first and last data points.
how much does a basket of apples weigh
Answers
Answer:
42-48 pound" number.
Step-by-step explanation:
FIRST ANSWER WILL GET 100 PTS!
What mixed number is equivalent to 21 ÷ 4?
Answers
Answer:
Step-by-step explanation:
5 1/4
Answer:là
5
với số dư
1
.
5
1
4
Step-by-step explanation:
How many real solutions does the system have ? y = - 3x - 1; y = x ^ 2 - 3x + 4
Answers
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The system of equations:
y = -3x - 1
y = x² - 3x + 4
The solutions of the equation.
y = 0
So,
-3x - 1 = 0
-3x = 1
x = -1/3
x² - 3x + 4 = 0
It is in the form of ax² + bx + c = 0
a = 1, b = -3, and c = 4
Now,
x = -b ± √(b² - 4ac) / 4a
x = 3 ± √(9 - 16) / 4
x = 3 ±√-7 / 4
x = 3 ±i√7 / 4
This is a complex root.
So,
These are not real solutions.
Thus,
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
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Old Navy had $940 worth of orders for shirts. The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos. The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops. Determine the number of each type of shirt ordered.
Answers
The number of each type of shirt ordered are as follows;
number of graphic tees = 29number of tanks tops = 19number of polos = 15How to find the number of each type of shirt ordered?Old Navy had $940 worth of orders for shirts.
The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos.
The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops.
let
x = number of graphic tees
Hence,
number of polos = 1 + 1 / 2 x
Number of tank tops = 1 / 2 x + 4
Therefore, the total
14x + 10(1 / 2 x + 4) + 22(1 + 1 / 2 x) = 940
14x + 5x + 40 + 22 + 11x = 940
30x + 62 = 940
30x = 878
x = 29.266667
x = 29
number of polos = 1 + 1 / 2 (29) ≈ 15
Number of tank tops = 1 / 2 (29) + 4 ≈ 19
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During a test, 3 out of 100 cars selected at random were found to be defective. Use this ratio to estimate the number of defective cars if 1,500 cars are tested.
Answers
There are 45 defective cars if 1,500 cars are tested.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities.
Given that;
During a test, 3 out of 100 cars selected at random were found to be defective.
Now,
Since, During a test, 3 out of 100 cars selected at random were found to be defective.
Let number of defective cars if 1,500 cars are tested = x
So, By definition of ratio, we get;
⇒ 3 / 100 = x / 1,500
Solve for x as;
⇒ 3 × 1500 / 100 = x
⇒ 3 × 15 = x
⇒ x = 45
Thus, There are 45 defective cars if 1,500 cars are tested.
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What number represents 3,675,100,608 rounded to the nearest million?
Answers
The number 3,675,000,000 represents 3,675,100,608 rounded off to the nearest million.
Rounding off large numbers.When we round off large numbers, we consider the digit to the right of the number occupying the place value for which we are rounding off to. If the digit to the right is 4 or less, we round down (we leave the number we are rounding to), but if the digit is 5 or higher, we round up (we increase the digit we are rounding by 1). and thus round to the indicated place value.
From the question, we have the large number;
3,675,100,608
the digit 5 indicates the place value (million)
and the digit 1 is to the right and will be rounded down.
Therefore, the number 3,675,000,000 represents 3,675,100,608, rounded to the nearest million.
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