Question

Given the exponential function f(x) = 60(1.07)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.

Exponential growth, 60% increase
Exponential growth, 7% increase
Exponential decay, 7% decrease
Exponential decay, 60% decrease

Answer 1

The answer is exponential, 7% increase

Explanation:

I completed the exam and got it correct. I hope it helps. :)

Answer 2

Exponential growth, 7% increase

Explanation:

we have

`f(x)=60(1.07)^(x)`

This is a exponential function of the form

`f(x)=a(b)^(x)`

where

a is the initial value

b is the base

If b > 1 ----> is a exponential growth

0 < b < 1 ----> is a exponential decay

r is the percent rate

`b=(1+r)`

In this problem we have

`a=60\\b=1.07`

1.07 > 1 -----> is a exponential growth

Find out the percent rate

`b=(1+r)\\1.07=1+r\\r=1.07-1\\r=0.07`

Multiply by 100 to convert a percent form

`r=0.07(100)=7\%`