Question

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. (5 points)

f(x) = 9.8 ⋅ 1.03x


Exponential growth function; 103%

Exponential growth function; 0.03%

Exponential growth function; 3%

Exponential decay function; 103%

Answer 1

Exponential growth function; 3%

Explanation:

Answer 2

Exponential growth function; 3%

Explanation:

The given function is
`f(x)=9.8(1.03)^(x)`

There are two expressions to indicate growth and decay, each equation is written like this:

• If the base of the function is between 0 and 1, the exponential function is a decay function.
• If the base of the function is more than 1, the exponential function is a growth function.

In this case, the given function is an exponential growth function, because 1.03>1. Therefore, the given function expresses decay.

The initial value of the function is when x = 0. Replacing initial value, we have:
`f(0)=9.8(1.03)^(0)=9.8`; which means that 9.8 is the initial value.

Also, the growing factor is 1.03, because is the base. In addition, the percentage rate of growth is given by:

Then,
`r=1.03-1=0.03`, which is a 3%.