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) = 2063 ⋅ 0.9953x


Exponential decay function; -0.47%

Exponential decay function; 0.0047%

Exponential growth function; 0.0047%

Exponential growth function; -0.47%

Answer 1

B. Exponential decay function; 0.0047%

Explanation:

We have been given an exponential function
`f(x)=2063\cdot 0.9953^x`. We are asked to find the constant rate of growth or decay.

We know that an exponential function is in form
`y=a\cdot b^x`, where,

a = Initial value,

For growth b is in form
`1+r` and for deacy b is in form
`1-r`.

Since b is less than 1, so our given function is an exponential decay function.

`1-r=0.9953`

`1-1-r=0.9953-1`

`-r=-0.0047`

`r=0.0047`

Therefore, our given function is an exponential decay function and option B is the correct choice.

Answer 2

When x increases by 1, f(x) decreases to 0.9953 of its previous value, a decrease of 0.47%.

The first selection is appropriate:

... Exponential decay function; -0.47%