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) = 2060 ⋅ 0.9906x

Exponential growth function; 0.0094%

Exponential decay function; -0.94%

Exponential decay function; 0.0094%

Exponential growth function; -0.94%

Answer 1

Exponential decay function; -0.94%

Explanation:

We are given an exponential function and we are supposed to find whether the given function increases or decreases and also the percentage of increase or decrease.

Th given function is f(x) = 2060
`* (0.9906)^(x)`

Here x denotes the number of years.

At the start the value was 2060. In the next year it was multiplied by 0.9906.

This means that the value becomes 0.9906 times after each year.

Hence the value decreases by 0.0094 times its original value.

Converting to percentage it becomes 0.94% decrease after each year.