Question

A function is shown below:

f(x) = (0.07)x

What does the function represent?
A. Exponential growth of 7%
B. Exponential decay of 7%
C .Exponential growth of 93%
D. Exponential decay of 93%

Answer 1

the function represents an exponential decay of 93%, as the number will enormously decrease in 0.93.

Answer 2

D. Exponential decay of 93%

Explanation:

We are given an exponential function
`f(x) = (0.07)^x`.

We know, the standard exponential function
`y= a(b)^x`, where a is the initial value and b is growth factor.

If b is greater than 1, then it would be an Exponential growth and if b is less than 1, then it would be an Exponential decay.

Also b= 1+r, where r is the rate of decay or growth.

For the given function
`f(x) = (0.07)^x`, we can see than b= 0.07.

0.07 is less than 1.

Therefore, it would be an Exponential decay.

Now, let us find rate of decay.

1+r = 0.07.

Subtracting both sides by 1, we get

r = 0.07-1 = -0.93.

In percentage it would be 93%.

Therefore, correct option would be

D. Exponential decay of 93%