04.03 HC)
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

(10 points)

Answers

Answer 1

Part A:

To find the average rate of change, let us first write out the equation to find it.

Δy/Δx = average rate of change.  

Finding average rate of change for Section A

Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5

Δx = 1- 0 = 1

Plug the numbers in: Δy/Δx = 5/1 = 5

Therefore, the average rate of change for Section A is 5.  

Finding average rate of change for Section B

Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

Δx = 3 - 2 = 1

Plug the numbers in: Δy/Δx = 36/1 = 36

Therefore, the average rate of change for Section B is 36.  

Part B:

(a) How many times greater is the average rate of change of Section B than Section A?

If Section B is on the interval [2,3] and Section A is on the interval [0,1].  

For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.  

(b) Explain why one rate of change is greater than the other.  

Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.


Related Questions

Find the value of x.
950°
1280°
60°

Answers

Answer:

x=77

Step-by-step explanation:

128+95+60+x=360

283+x=360

x=77

is ( -5, 6) ( -2, 0) ( 0, 6) ( 0, 2) ( 1, -3) a function

Answers

Answer:

No

Step-by-step explanation:

No, ( -5, 6) ( -2, 0) ( 0, 6) ( 0, 2) ( 1, -3) do not make up a function. It does not pass the vertical line test when graphed, as there are 2 points, (-5, 6), and (0, 6), that lines up on the same y-value.

A raised flower bed is 40 feet​ long, 7 feet​ wide, and 1.2 feet deep. Find the area of the bed and the volume of soil it holds.

Answers

Area = length x width

Area = 40 x 7 = 280 square feet

Volume = length x width x depth

Volume = 40 x 7 x 1.2 = 336 cubic feet

At the movie theatre, child admission is $5.50 and adult admission is $8.90. On Friday four times as many adults tickets as child tickets were sold, for a total sales of $986.40. How many child tickets were sold that day?

Answers

Answer:

You can use grouping, quantity and value to solve this question.

Child admission = $5.50

Adult admission = $8.90

Friday sales (Quantity):

Child = x

Adult = 4x

Total sales = 5x

Friday sales (Value):

Child = $5.50

Adult = 4 × $8.90

         = $35.60

Total sales = $986.40

1 group = $5.50 + $35.60

            = $41.10

Number of groups = $986.40 ÷ $41.10

                               = 24

The number of child tickets sold is 24.

Express sin UU as a fraction in simplest terms.
S
T
U
24
18

Answer: \sin U =sinU=


Answers

The expression of sinU as a fraction is 12/13

Find the diagram attached.

To get the fraction represented by sinU, we will use the SOH CA TOA identity.

From the diagram;

Hypotenuse = SU = 13Opposite = ST = 12 (angle opposite to m<U)

Since sin theta = opp/hyp

SinU = ST/SU

SinU = 12/13

Hence the expression of sinU as a fraction is 12/13

Learn  more on SOH CAH TOA here: https://brainly.com/question/20734777

Find X. Enter a number for your answer. Do not type the symbol for degree or the
word "degrees"

Answers

Use angle sum property (the 3 angles in a triangle sum up to 180°).

2x + x + 54 = 180

3x + 54 = 180

3x = 180 - 54

3x = 126

x = 126/3

x = 42

_____

Hope it helps ⚜

Answer:-

x = 42

Explanation:-

We know that,

Angles of a triangle adds to 180°

So,

=> 2x + x + 54 = 180

=> 3x = 180 – 54

=> 3x = 126

=> x = 126/3

=> x = 42

(x = 42° ; 2x = 84°)

2. Harry puts $5 in his piggy bank every
week. What type of slope does this
scenario describe? Explain.

Answers

Answer:

linear

Step-by-step explanation:

Answer:

Linear slope of 5/1

Step-by-step explanation:

The rate is constant.

Hope that helps

Help me with this question thanks so much

Answers

It would be 6^8 or 1,679,616
Since it’s times 6 each time and the base is 6 it can be written as an exponent 6*6*6...
Hope that helps :)

Which equation represents this statement?

The product of 1/5 and a number is equal to 1/1 2.


1/5n=1/1 2

1/5÷n=1/1 2

1/5−n=1/1 2

1/5+n=1/1 2

Answers

Answer:

answer is B

Step-by-step explanation:

William is trying to pay off his credit card bill. He currently owes $184 on his bill without the interest charge from the credit card company. If the company charges 8% interest on his credit card bill, how much will William need to pay the credit card company so that he will have no payments?

Answers

Answer:

$198.72

Step-by-step explanation:

help. i need itttttt

Answers

Answer:

In a parallelogram, opposite sides are the same length. If PR  = ST, then the same would happen for the other sides.

Step-by-step explanation:

please help i have a few minutes left!!
A. {a, c, g, j, k, r}
B. {C, g)
C. {a}
D. {a, c, g, j, q, k, r}

Answers

Answer:

Short

"Option A is the answer"

pls help due tonight

Answers

Answer:

-32

Step-by-step explanation:

-32x + 4y = 12

4y = 12 + 32x

/4      /4     /4

y = 3 + 8x

solve 557+3 using number disks

Answers

557+3=560 cuz 57+3 = 60 and 60+500= 560

2x2 +5x+8
Given x 3-2, the expression
x+2.
is equivalent to

Answers

Answer:

x=-1

Step-by-step explanation:

so 3-2 is 1 right so what humber + 2 is 1 well -1 becasue -1 + 1 is 0 and plus 2 would be 1 so its -1 (or x= -1). Hope this helped!

The expression equivalent to the given expression is (2x+1)+6/(x+2)

What is an expression?

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, (2x²+5x+8)/(x+2)

From the given options,

Simplifying (2x+1)+6/(x+2), we get,

= (2x+1)(x+2)+6/(x+2

= (2x²+4x+x+6+2)/(x+2)

= (2x²+5x+8)/(x+2)

Since, we get the main expression by solving the option expression,

Hence, the expression equivalent to the given expression is (2x+1)+6/(x+2)

For more references on expressions, click;

https://brainly.com/question/14083225

#SPJ2

Anna categorized her spending for this month into four categories: Rent, Food, Fun, and Other.

If Anna spent a total of $2900 this month, how much did she spend on Rent?

Answers

Answer:

.26 * 2900= 754 dollars

Step-by-step explanation:

I'm not sure if it's right.

Using the slope formula, find the slope of the line through the points (0,0) and (4,8).
Use pencil and paper. Explain how you can use mental math to find the slope of the line. (please show how to do on pencil and paper)

Answers

Answer:

[tex]m = 2[/tex]

Step-by-step explanation:

Using mental math to find the slope of the line:

If you think about the formula, then you set up the points in your head, you will notice that the first point is on top of the second point. And that way makes it easy to simplify. All you would need to do is subtract down in your head: For example:

(0, 0)

(4, 8)

As you can see, the first point is on top of the other, and that way you can just subtract from bottom to top. If you do it that way, it is set up (Remember, you would do this all in your head)

NEED NOW PLEASE.......

Answers

Answer:

Integers

Step-by-step explanation:

Integers are the set of whole numbers and their opposites.

The answer is integers

Sammy's rabbit can eat 70 pounds of food in 80 days. Part A: At that same rate, how much food will Sammy need to feed his rabbit in 24 days? Part B: How long will it take his rabbit to eat 87.5 pounds of food? Part C: Suppose Sammy buys his rabbit a companion. Together, the rabbits need can eat 95 pounds of food in 65 days. Approximately how much food will Sammy need to buy in order to feed both rabbits inl year ( 365 daya)? Round to the nearest tenth.​

Answers

Part A

The rabbit can eat 70 pounds of food in 80 days. The unit rate is 70/80 = 0.875 pounds of food per day. Multiply this with the 24 days to get the total amount eaten over that timespan.

24*0.875 = 21

Answer:  21 pounds of food

=========================================================

Part B

x = number of days

The rabbit eats at a unit rate of 0.875 pounds per day. After x number of days pass by, the rabbit has eaten a total of 0.875x pounds of food. Set this equal to 87.5 and solve for x.

0.875x = 87.5

x = (87.5)/(0.875)

x = 100

Answer: 100 days

=========================================================

Part C

This is is similar to part A, just with different numbers. We could follow those steps to get the answer, but I'll go another route.

Instead, I'll use a proportion to solve.

(95 pounds)/(65 days) = (x pounds)/(365 days)

95/65 = x/365

95*365 = 65*x

34675 = 65x

65x = 34675

x = 34675/65

x = 533.461538

x = 533.5

Answer: 533.5 pounds of food

answer part B and yeaa don’t mind my answers

Answers

Answer:

you are correct

Step-by-step explanation:

Greg is a novice cook trying to perfect his baked potato recipe. He decides to put
many. potatoes in the oven and invites all his friends over. Every few minutes he
takes a potato out of the oven and asks some friends to rate its taste on a scale
from 1 to 10, where 10 is excellent.
For each taste, Greg writes down the number of minutes the potato spent in the
oven, x, as well as its rating from 1 to 10, y.
The least squares regression line of this data set is:
y = 0.109x + 1.437
What rating does this line predict for a potato spending 67.11 minutes in the oven?
Round your answer to the nearest integer,

Answers

2.079 I think? I’m sorry if I’m wrong I haven’t done this in years and I just wanna help….

If △CFE≅△PTR, complete each of the following statements:

CE¯¯¯¯¯¯¯¯ ≅

TR¯¯¯¯¯¯¯ ≅


∠P ≅∠

∠F ≅∠


△FEC ≅△

△RPT ≅△

Answers

Based on the definition of congruent triangles, the statements will be completed as follows:

CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECF

Recall the following about Congruent Triangles:

The three angles of one triangle is congruent to the three corresponding angles in another triangle if both triangles are congruent triangles.The three sides of one triangle is congruent to the three corresponding sides in another triangle if both triangles are congruent triangles.

Given that △CFE≅△PTR, thus:

CE corresponds to PR, therefore CE ≅ PRFE corresponds to TR, therefore FE ≅ TRCF corresponds to PT, therefore CF ≅ PT∠P corresponds to ∠C, therefore ∠P ≅ ∠C∠T corresponds to ∠F, therefore ∠T ≅ ∠F∠R corresponds to ∠E, therefore ∠R ≅ ∠E

Thus, based on the definition of congruent triangles, the statements will be completed as follows:

CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECF

Learn more about congruent triangles on:]

https://brainly.com/question/8876876

pls help i need help with this been working fo a bit

Answers

[tex]\\ \sf\Rrightarrow \dfrac{6}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}(y+x)[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{6}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}x+\dfrac{5}{7}y[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{6}{7}x+\dfrac{5}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}y[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{11}{7}x+\dfrac{-14+25}{35}y[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{11}{7}x+\dfrac{11}{35}y[/tex]

Done!

[tex] \boxed{\huge \bf \: Question:—}[/tex]

[tex] \sf \longmapsto \: \dfrac{6}{7} x - \dfrac{2}{5} y + \dfrac{5}{7} (y + x)[/tex]

[tex]\boxed{\huge\bf \: Solution:—}[/tex]

[tex] \boxed{\bf \: Distribute:—}[/tex]

[tex]\sf \longmapsto \: \dfrac{6}{7} x - \dfrac{2}{5} y + \dfrac{5}{7} y + \dfrac{5}{7} \: x[/tex]

[tex]\sf \longmapsto \dfrac{6}{7} x + \dfrac{ - 2}{5} y + \dfrac{5}{7} y \: + \dfrac{5}{7} x[/tex]

[tex] \boxed{\bf \: Combining \: Like \: Terms:—}[/tex]

[tex]\sf \longmapsto\dfrac{6}{7} x + \dfrac{ - 2}{5} y + \dfrac{5}{7} y \: + \dfrac{5}{7} x[/tex]

[tex]\sf \longmapsto \bigg(\dfrac{6}{7} x + \dfrac{5}{7} x \bigg) \: + \bigg( \dfrac{ - 2}{5} y + \dfrac{5}{7} \: y \bigg)[/tex]

[tex]\sf \longmapsto \: \dfrac{11}{7} x \: + \dfrac{11}{35} y[/tex]

[tex]\boxed{\bf \: Answer:—}[/tex]

[tex] \boxed{\bf \: \dfrac{11}{7} x \: + \dfrac{11}{35} y}[/tex]

Find the equation of the line

Answers

Answer:

Y = 4x - 9

Step-by-step explanation:

Hope this helps! If it’s wrong I’m really sorry.

Pls give brainliest!

Answer:

...

Step-by-step explanation:

identify whether the given mathematical sentences below is true or false, then write your reason. If false , write the correct answer.​

Answers

Answer:

Step-by-step explanation:

The sum of a number times 7 and 15 is at least -19

Answers

Answer:

x(7+15) [tex]\leq[/tex] -19

Step-by-step explanation:

Alyssa needs 4 pieces of wood that are 12 inches long to build a box. She bought a length of wood that was 60 inches long. How much extra wood does she have?

Answers

Answer:

She has 12 inches wood left

Step-by-step explanation:

1. As a diver descends, the pressure in the water
a
increases by about 0.455 pound per square
inch
(psi) for each foot of descent. This can be
modeled by the equation P = 0.455d + 14.3,
where P is the pressure in pounds per square
inch and d is the depth in feet.
Use a graphing calculator to graph the model.
(a)
Sketch the graph showing d (horizontal axis
representing depth )and P (vertical axis
representing the pressure).

Answers

Plotting the graph using geogebra online graphing tool and attaching.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let P represent the pressure in pounds and d represent the depth in feet.

Given the equation:

P = 0.455d + 14.3

Plotting the graph using geogebra online graphing tool and attaching.

Find out more at: https://brainly.com/question/13911928

3. A recipe for banana cakes calls for 6 cups of mashed banana to 9 cups of flour. How many cups of
flour per cup of mashed banana does the recipe require?

Answers

3 cups of flour for every 2 bananas
3:1

A polygon with both equal angles and equal sides is called

Answers

Answer:

It's called a regular polygon

Answer:

A regular Polygon

Step-by-step explanation:

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