Question

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

f(x) = 3.6 ⋅ 1.04x

Answer 1

Exponential growth; percentage rate of growth is 4%.

Explanation:

The function,

`f(x)=3.6.(1.04)^x`

represents an exponential growth function because the growth factor is greater than 1.

The general form of an exponential growth function is,

`y=a(1+r)^t=(a).(ar)^t`, where 'r' is the percentage rate of growth.

If we compare the given equation with the standard form of the equation we can see that, we have,

`f(x)=3.6(1+0.04)^x`

Therefore, the percentage rate of growth is =
`0.04 * 100=4\%` .