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

Answer:

Exponential growth, 7% increase

Step-by-step 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

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