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25 POINTS
answer question 4 pleaseeeee

25 POINTS answer question 4 pleaseeeee-example-1
User Alex Ball
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1 Answer

4 votes

Answer:

a) The average rate of change for the function
f(x)=4(2)^x over interval x=1 to x=2 is 8

b) The average rate of change for the function
f(x)=4(2)^x over interval x=3 to x=4 is 32

Explanation:

We are given function
f(x)=4(2)^x

We need to find Average rate of change

The formula used is:
Average \ rate \ of \ change=(f(b)-f(a))/(b-a)

Part a) The interval is: x=1 to x=2

We have a= 1 and b=2

Finding f(a) i.e f(1)


f(x)=4(2)^x\\Put \ x =1\\f(1)=4(2)^1\\f(1)=4(2)\\f(1)=8

Now finding f(b) i.e f(2)


f(x)=4(2)^x\\Put \ x =2\\f(2)=4(2)^2\\f(2)=4(4)\\f(2)=16

Now finding average rate of change.


Average \ rate \ of \ change=(f(b)-f(a))/(b-a)\\Average \ rate \ of \ change=(16-8)/(2-1) \\Average \ rate \ of \ change=(8)/(1)\\Average \ rate \ of \ change=8

So, average rate of change for the function
f(x)=4(2)^x over interval x=1 to x=2 is 8

Part b)

The interval is: x=3 to x=4

We have a= 3 and b=24

Finding f(a) i.e f(3)


f(x)=4(2)^x\\Put \ x =3\\f(3)=4(2)^3\\f(3)=4(8)\\f(3)=32

Now finding f(b) i.e f(4)


f(x)=4(2)^x\\Put \ x =4\\f(4)=4(2)^4\\f(4)=4(16)\\f(4)=64

Now finding average rate of change.


Average \ rate \ of \ change=(f(b)-f(a))/(b-a)\\Average \ rate \ of \ change=(64-32)/(4-3) \\Average \ rate \ of \ change=(32)/(1)\\Average \ rate \ of \ change=32

So, average rate of change for the function
f(x)=4(2)^x over interval x=3 to x=4 is 32

Since the interval is increasing, so does our average rate of change increasing as function is also increasing.

User Erdi
by
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