Question

Terrance invested money in a technology stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of days. Find the approximate average rate of change from day 3 to day 8.

A 0.496
B 2.016
C 2.48
D 5

Answer 1

Answer: A, 0.496

Step-by-step explanation:

To find the difference, you need to raise the base, 2, to each number since x represents the days.

Raise 2 to the power of 3:

2^3 = 8

multiply by 0.01

0.01 * 8 = 0.08

That is the growth of day three.

Now do the same with the 8

Raise 2 to the power of 8

2^8 = 256

Now multiply that by 0.01

0.01 * 256 = 2.56

Now use this formula: f(b) - f(a)/b - a

2.56 - 0.08/8 - 3

Subtract 0.08 from 2.56

2.56 - 0.08 = 2.48

Subtract 3 from 8

8 - 3 = 5

Now divide: 2.48/5 = 0.496

0.496 is the average rate of change between day 3 and day 8. Also I got 100 on the test so I know the answer :))

Answer 2

Option A 0.496

Explanation:

we know that

The approximate average rate of change is equal to

`(f(8)-f(3))/(8-3)`

`(f(8)-f(3))/(5)`

we have

`f(x)=0.01(2^(x))`

Find f(8)

For x=8

`f(8)=0.01(2^(8))=2.56`

Find f(3)

For x=3

`f(8)=0.01(2^(3))=0.08`

Find the approximate average rate of change

`(f(8)-f(3))/(5)`

substitute

`(2.56-0.08)/(5)=0.496`