Find C and a so that ​f(x)equalsCa Superscript x models the situation described. State what the variable x represents in your formula. There are initially 3000 ​bacteria, and this sample doubles in size every hour.

Answers

Answer 1

Answer: x represents the time period.

C= 3000 and a = 2

Step-by-step explanation:

The given equation is [tex]f(x)=Ca^x[/tex] which is an exponential equation. (i)

The general form of the exponential equation is :

[tex]f(x)=Ab^x[/tex]   (ii)

, where A = initial value and b= multiplicative factor, and x is the time.

As compare both of the equation in (i) and (ii) , we get

A= C , and b= a

Since there are initially 3000 ​bacteria, and this sample doubles in size every hour.

i.e. C= 3000 (Initial)  and a= 2 (multiplicative factor).


Related Questions

Gwen is travelling to another country. She flies for 3 hours at an average speed of 625 km/h on one plane. She then flies for 4 hours 15 minutes at an average speed of 880 km/h on a second plane. What is the total distance, in km, she travelled by plane?

Answers

Answer:

5,615 km.

Step-by-step explanation:

The first flight, she traveled for 3 hours at a speed of 625 km/h.

[tex]\frac{625}{1} =\frac{x}{3}[/tex]

x = 625 * 3

x = 1,875.

The first flight, she traveled 1,875 km.

The second flight, she traveled for 4.25 hours at a speed of 880 km/h.

[tex]\frac{880}{1} =\frac{x}{4.25}[/tex]

x = 880 * 4.25

x = 3,740.

The second flight, she traveled 3,740 km.

So, in total, she traveled 1875 + 3740 = 5,615 kilometres.

Hope this helps!

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using Pythagoras theorem, caclutale AC AB=11cm BC=4CM AC=unknown using Pythagoras theorem, caclutale the length of AC

Answers

Answer:

11.70 cm

Solution,

AB (p) = 11 cm

BC (b) = 4 cm

AC (h) = ?

now,

Using the Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {h}^{2} = {(11)}^{2} + {(4)}^{2} [/tex]

[tex] {h }^{2} = 121 + 16[/tex]

[tex] {h }^{2} = 137[/tex]

[tex]h = \sqrt{137} [/tex]

[tex]h = 11.70 \: cm[/tex]

Hope this helps...

Good luck on your assignment..

In the diagram below, AB is parallel to CD. What is the value of x?

Answers

Answer:

150 degrees

Step-by-step explanation:

You can figure this out by looking at the degrees below d, and you see it is thirty, and that it is equal to the degree above the x, so then you subtract 30 from 180 to get 150. Hopefully that makes sence, I forgot what some of the terms are called.

translate 22% of b into an expression

Answers

Answer:

11/50b

Step-by-step explanation:

22% of b = 22/100×b

= 11/50b

There are 8 red, 8 blue and 8 yellow marbles in a jar. What is the fewest marbles you can remove from the jar so that the ratio of red to non-red marbles is 3 to 7 and so that the ratio of yellow to non-yellow marbles is also 3 to 7?

Answers

Answer:

5 red, 5 yellow, and 4 blue

Step-by-step explanation:

Answer:

5 red, 5 yellow, and 4 blue :)

Step-by-step explanation:

Length: 4 - 7(3x + 4y)
Width: 3x(-2y)
Write a simplified expression for the perimeter of the rectangle.
___ - x - ___y - ___xy

Answers

8 - 42x - 56y - 12xy

An insurance company is trying to determine the number of phone calls made weekly while driving. Which best describes the population?

Answers

Answer: Taking a poll of how many calls someone took anonymously and randomly choose 100 people

Step-by-step explanation:

Answer:

licensed drivers who own cell phones

Step-by-step explanation:

licensed drivers who own cell phones

In this system of equations, which variable would it be easiest to solve for? x + 3 y = 13. 3 x + 2 y = 25. The easiest to solve for is x in the first equation. The easiest to solve for is y in the first equation. The easiest to solve for is x in the second equation. The easiest to solve for is y in the second equation.

Answers

Answer:

its x in the first equation! (a)

Step-by-step explanation:

I just took the test. I used the other answer but it was wrong :( BUT  you can trust me :)    

Answer:

A: The easiest to solve for is x in the first equation.

Step-by-step explanation:

The X in the first equation is the only one without a coefficient.

Is the following relation a function?

Answers

Answer:

No because y repeats with a diffirent x i think

Step-by-step explanation:

If it doesn't bother you would you let me know if i was right?

It takes 1 hour (t) to fill the water tank of volume (V) 750 m3. Identify the dependent and the independent variables.

Answers

Answer:

The time t is the independent variable while the volume V is the dependent variable

Step-by-step explanation:

A variable is a parameter that changes.

We have two types namely dependent and independent variables.

A dependent variable is a variable which its value needs to be determined based on the value of another variable while and independent variable is a variable which its value independent of other parameters.

In our question, It takes 1 hour (t) to fill the water tank of volume (V) 750 m3.

The volume of the tank V changes as time changes. So the volume of the tank V is dependent on time, t.  

So V is proportional to t

Since the volume of the tank is the variable that needs to be determined based on another variable-which is time,t- it is the dependent variable, while the time,t is the independent variable since its value is not determined based on other parameters.

the number 144 is multiplied with 2^-3 , 12^-1 and 3^-2 consecutively . Find the final product pls quick :)

Answers

Answer:

[tex]\boxed{\sf \ \ \ \dfrac{1}{6} \ \ \ }[/tex]

Step-by-step explanation:

Hello

when you multiply by [tex]2^{-3}[/tex]

it is equivalent to divide by [tex]2^3[/tex]

so we are looking for

[tex]144*2^{-3}*12^{-1}*3^{-2}=\dfrac{144}{2^3*12*3^2}=\dfrac{9*16}{2^3*12*3^2}\\=\dfrac{3^2*2^4}{2^3*12*3^2}=\dfrac{2}{12}=\dfrac{1}{6}[/tex]

hope this helps

do not hesitate if you have any question

The volume of a rectangular prism is 240 cubic centimeters. A rectangular pyramid has the same length, width, and height as the prism. What is the volume of the pyramid?

Answers

Answer:

The volume of the pyramid is 80 cubic centimeters.

Step-by-step explanation:

As the formula for the volume of a pyramid is 1/3bh, so if all the dimensions are the same for both figures, just divide the volume of the prism by three to find the volume of the pyramid. If you do this 240÷3=80 or the volume of the pyramid.

Answer:

80 cubic centimetres

Step-by-step explanation:

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height.

Here, we know that the prism's volume is 240, so lwh = 240.

The volume of a rectangular pyramid is denoted by V = (1/3) * lwh, where l is the length of the rectangular base, w is the width of the rectangular base, and h is the height.

We know that the length, width, and height of the pyramid are the same as those of the prism, so we want to simply find V = (1/3) * lwh. From the prism, we see that lwh = 240, so plug that in:

V = (1/3) * lwh

V = (1/3) * 240 = 80

The answer is thus 80 cubic centimetres.

~ an aesthetics lover

if the redius of a circle is 5cm what is the circumference​

Answers

Answer:

10π

Step-by-step explanation:

Circumference formula is : 2πr

So if you put r into this formula, it will be: 2π5

Now, you can multiply 2 by 5 to get 10, leaving you with 10π

Answer:

10 π

Step-by-step explanation:

The formula for circumference is C=2 πr, where r is radius, so if we do C=2 π(5), we get C=10 π

A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the arc is °.Which angle measure less than or equal to 360° is equivalent to an angle of ?

Answers

Answer:

  320°

Step-by-step explanation:

Part 1

The arc length is given by ...

  s = rθ . . . . . r is the radius, θ is the central angle in radians

We want to find θ, so we can fill in the given values and divide by the coefficient of θ.

  8π = 4.5θ

  θ = 8π/4.5 = 16π/9 . . . radians

Since π radians = 180°, the degree measure of the angle is ...

  θ = (16/9)180° = 320°

The measure of the angle subtended by the arc is 320°.

_____

Part 2

We might be able to help with the second part of the question, but you need to edit to put in the numbers and answer choices.

I thought of a number. I added one, divided by 3 and got 6. What was my number?

Answers

Answer:

17

Step-by-step explanation:

6 x 3 = 18

18 - 1 = 17

Hope this helps.

Working backwards always works.

6th grade math heeelppppppppp :D

Answers

Answer:

5(6x+3y) is equalivent to 30x+15y

Answer:

30x+15y

Step-by-step explanation:

distributive property

5 The absolute value of 9 is 9.
O True
O False​

Answers

Answer: True

Explanation:

absolute value is always positive and represents the values distance from zero. The absolute of 9 and -9 are both 9.

Answer:

True

Step-by-step explanation:

The absolute value of a number is its distance from zero on the number line. The distance of 9 from 0 is 9.

X= 3y-5
2x + 12y = -4
This is a system of equations can somebody solve it you can use any method ​

Answers

Answer:

x = -4, y = 1/3

Step-by-step explanation:

=> x = 3y-5        (Equation 1)

=> 2x+12y = -4  (Equation 2)

Putting (1) in (2)

=> 2(3y-5)+12y = -4

=> 6y-10+12y = -4

=> 18y = -4+10

=> 18y = 6

Dividing both sides by 18

=> y = 6/18

=> y = 1/3

Putting y = 1/3 in Equation 1

=> x = 3(1/3)-5

=> x = 1-5

=> x = -4

x=3y-5
2x+12y=-4

(-2)x=-6y+10
2x+12y=-4
12y=6
y=1/2

x=3y-5
2x+12y=-4

(-4)x=-12y+20
2x+12y=-4
-2x=16
x=-8

Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas for a total of 152 slices. Let c represent the number of cheese pizzas and let v represent the number of vegetable pizzas. Which equation represents the relationship between the number of cheese pizzas and the number of vegetable pizzas? Which equation represents the total number of pizza slices?

Answers

Answer:

Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas for a total of 152 slices. Let c represent the number of cheese pizzas and let v represent the number of vegetable pizzas.

Which equation represents the relationship between the number of cheese pizzas and the number of vegetable pizzas?

✔ c = 4v

Which equation represents the total number of pizza slices?

✔ 8c + 6v = 152

The equation that the number of cheese pizzas and the number of vegetable pizzas is c = 4v

And, the  equation represents the total number of pizza slices is 8c + 6v = 152

Given that,

Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas for a total of 152 slices. Let c represent the number of cheese pizzas and let v represent the number of vegetable pizzas.

Based on the above information, the equation is as follows:

c = 4v

8c + 6v = 152

Learn more: https://brainly.com/question/1301963?referrer=searchResults

Simplify 3 : 18 the following in to the form 1 : n

Answers

Answer:

1 : 6

Step-by-step explanation:

3 : 18

3 ÷ 3 : 18 ÷ 3

1 : 18 ÷ 3

1 : 6

Answer:

n=6

Step-by-step explanation:

3:18

1:6

3/1=3

18/3=6

A car travels 18m in one second. How far will it travel in one hour at the same rate ?​

Answers

Answer:

64800

Step-by-step explanation:

you will multiply 60 by 18m to get how much you go in a minute. and then you multiply that by 60 again to get how much you go in an hour.

Answer:

64800

Step-by-step explanation:

18x60= 1080

1080x60= 64800

explain how to solve 2x+9=15

Answers

Answer:

I hope it will help you :)

Find the equation of the line through point (−7,2) and parallel to y=25x−12. Use a forward slash (i.e. "/") for fractions (e.g. 1/2.

Answers

parallel line so gradient stays the same at 25x

y=25x+c

substitute in the point

-7= 25(2) +c

-7 = 50 + c

(-7)-50= -57

y=25x-57

hope this helps!

The equation of the line in slope intercept form is y = 25x + 177.

What is equation of a line?

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

For the given situation,

The equation is y = 25x−12 -------- (1)

The point is (−7,2)

The general form of equation of line in slope intercept form is

[tex]y=mx+c[/tex]

On comparing this equation with equation, we get

slope, m = 25

The given line is parallel to the equation of line, so slope is same.

The line passes through the point (x1, y1) is (−7,2).

Thus the equation of line in slope intercept form is

[tex]y-y1=m(x-x1)[/tex]

⇒ [tex]y-2=25(x-(-7))[/tex]

⇒ [tex]y-2=25(x+7)[/tex]

⇒ [tex]y-2=25x+175[/tex]

⇒ [tex]y=25x+175+2[/tex]

⇒ [tex]y=25x+177[/tex]

Hence we can conclude that the equation of the line in slope intercept form is y = 25x + 177.

Learn more about equation of line here

https://brainly.com/question/19546232

#SPJ3

The table below shows some inputs and outputs of the invertible function f with domain all real numbers. NEED HELP NOW!!!!!

Answers

Answer:

( 1 ) [tex]f^{-1}(f(576)) = 576[/tex],

( 2 ) [tex]f^{-1}(-7)+f(-7) = 13[/tex]

Step-by-step explanation:

Taking the function and it's inverse, it should be the following property -

[tex]f^{-1}(f(x))= x[/tex] - this therefore makes the functionality " [tex]f^{-1}(f(576))= x[/tex] " equivalent to 576 itself.

For this second part here let's consider the portion " [tex]f(-7)[/tex] " firstly. As you can see from the table, - 7 should represent the x - value, hence [tex]f(-7) = 7[/tex]. Now for this second bit here, we have to take the inverse - making the what should have been the x - value, now the f( x ) value. Therefore, [tex]f^{-1}(-7) = 6[/tex].

This would make [tex]f^{-1}(-7)+f(-7)[/tex] = [tex]7+6[/tex] = 13.

Which statement is true

Answers

Answer:

C

Step-by-step explanation:

in order of containment it goes

Quadrilaterals

Parallelograms and trapezoids

kites rhombuses and rectangles

squares

Answer:

Hey there!

All parallelograms are four sided shapes, also called quadrilaterals.

Hope this helps :)

Complete the solution of the equation. Find the
value of y when x equals 5.
-6x – 3y = -57
Enter the correct answer.​

Answers

Answer:

y = 9

Step-by-step explanation: this is because when x is 5 and is multiplied by -6 u get -30. from there u substratc -30 from -57 and get -27. so y is 9

What is the line of best fit? Why do we want the sum of the residuals to be as close to zero as possible?

Answers

Answer:

Step-by-step explanation:

A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.

The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.

x = 2y - 3 & 3x - 7y = -14

Answers

Answer:

(7, 5)

Step-by-step explanation:

You can solve by substitution

3(2y - 3) - 7y = -14

6y - 9 - 7y = -14

-y - 9 = -14

-y = -5

y = 5

x = 2(5) - 3

x = 7

Answer:

(7, 5).

Step-by-step explanation:

x = 2y - 3

2y = x + 3

y = x/2 + 3/2

3x - 7y = -14

-7y = -3x - 14

y = 3/7x + 2

3/7x + 2 = 1/2x + 3/2

6/14x - 7/14x = 1.5 - 2

-1/14x = -1/2

1/14x = 1/2

x = 7

7 = 2y - 3

2y = 10

y = 5

3 * 7 - 7 * 5 = 21 - 35 = -14

Since this works, your answer will be (7, 5).

Hope this helps!

WILL GIVE BRAINLIEST AND 21 POINTS! Calculate the area of the triangle: A =

Answers

Answer:

area: 27

Step-by-step explanation:

Sides: a = 10.296   b = 14.213   c = 6

The calculation of the triangle progress in two phases. The first phase is such that we try to calculate all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase is the calculation of other characteristics of the triangle, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

Only answer if you are sure thanks!

Answers

Answer:

B. (0,0)

Step-by-step explanation:

Answer:

B. (0, 0).

Step-by-step explanation:

The parent function is y = x^2.

The vertex is at the minimum value of this, that is when x = 0 and y = 0.

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