Question

Which functions are exponential growth functions? choose exactly two answers that are correct.

1. f(x)=0.75^
2.g(x)=(3/2)^
3.h(x)=1.08^
4.j(x)=(1/3)^

please answer correctly ​

Answer 1

2.g(x)=(3/2)^x

3.h(x)=(1.08)^x

Explanation:

We are required to find the exponential growth function.

As, we know,

Exponential growth function is of the form,
`F(x)=(1+r)^x`, where r is the rate of growth.

If 'r' is positive, then the function is a growth function and if 'r' is negative, then the function is a decay function.

So, comparing the options, we have,

1.
`f(x)=(0.75)^x` i.e.
`f(x)=(1-0.25)^x`

So, the function is not a growth function.

2.
`g(x)=(3/2)^x = (1.5)^x` i.e.
`g(x)=(1+0.5)^x`

So, the function is an exponential growth function.

3.
`h(x)=(1.08)^x` i.e.
`h(x)=(1+0.08)^x`

So, the function is an exponential growth function.

4.
`j(x)=(1/3)^x=(0.33)^x` i.e.
`j(x)=(1-0.67)^x`

So, the function is not a growth function.

Hence, the growth functions are
`g(x)=(3/2)^x` and
`h(x)=(1.08)^x`.

So, options 2 and 3 are correct.