Question

Which of these values for p and a will cause the function f(x)=Pax to be an exponential growth function

Answer 1

Its P = 1/5 ; a = 2

Explanation:

I am doing the test; I got it right.

Answer 2

The option are missing in the question. The options are :

A. P = 2, a = 1

B.
`$P=(1)/(2) ; a =(1)/(3)$`

C.
`$P=(1)/(2) ; a =1$`

D. P = 2, a = 3

Solution :

The given function is
`$f(x)= Pa^x$`

So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.

When the four option being substituted in the function, we get

A). It is a constant function since
`$2(1^x)=2$`

B). Here, the value of a is a fraction which is less than 1, so it is a decay function.
`$f(x)=(1)/(2)\left((1)/(3)\right)^x$`

C). It is a constant function since the value of a is 1.

D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.

`$f(x)=2(3)^x$`

Therefore, option (D). represents an exponential function.