Question

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. (2 points) f(x) = 7.2 ⋅ 1.08x

Answer 1

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: amount or initial value

b: rate of change

x: independent variable

y: dependent variable

We have two possible cases:

If 0 <b <1:

The exponential function is decreasing

if b> 1:

the exponential function is increasing.

For this case we have the following function:

$f (x) = 7.2 * (1.08) ^ x$

For this case we have to:

$b = 1.08$

Therefore, the exponential function is increasing.

The percentage of growth is:

$(1.08-1) * (100) = 8%$

Answer:

The exponential function is increasing.

The exponential function grows 8% for each value of x.