Question

The equation y = 200(1.06)X models an exponential function. Determine if the

function is growth or decay and find the growth or decay rate.

Answer 1

Given:

The given function is

`y = 200(1.06)^x`

To find whether the function is growth or decay and the growth of decay.

Formula:

The function
`a(1+r )^x` is said to be an exponential growth, if the value of a > 0 and r > 0

Again, the function
`a(1-r )^x` is said to be an exponential decay, if the value of a > 0 and 0 < r < 1.

Now,

`y = 200(1.06)^x`

`y = 200(1+0.06)^x`

Thus, the value of a > 0 and r > 0, then the given function is an exponential growth function.

Therefore,

The given function is an exponential growth function.