Question

Given the exponential function f(x) = 16(0.75)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.

Answer 1

Answer:

The answer is Exponential decay, 25% decrease

Step-by-step explanation:

In f(x) = 16(0.75)x the (0.75) does not have a 1 so it is decreasing and if it is only 75% of 16 then it would be losing 25% each time

Answer 2

An exponential function can either represent a growth or decay

The function represents decay, and the percentage rate of decay is 75%

An exponential function is represented as:

$\mathbf{f(x) = ab^x}$

if b > 0, then the function represents growth;

Otherwise, it represents decay

The function is given as:

$\mathbf{f(x) = 16(0.75)^x}$

By comparison:

$\mathbf{ b= 0.75}$

This means that the function represents decay

The percentage rate (r) of decay is then calculated as:

$\mathbf{r= 1 - b}$

So, we have:

$\mathbf{r= 1 - 0.25}$

$\mathbf{r= 0.75}$

Express as percentage

$\mathbf{r= 75\%}$

Hence, the percentage rate (r) of decay is 75%

Read more about exponential functions at:

https://brainly.com/question/3127939