Question

Which of the following represents Exponential Growth? Choose all that apply.

Group of answer choices
y=(5/4)^x

y=4^-x

y=5^x

y=(4/5)^x

Answer 1

`y=((5)/(4))^x`

`y=5^x`

Explanation:

we know that

In a exponential function of the form

`y=a(b^x)`

where

a is the initial value

b is the base

If the value of b >1 ----> then is a exponential growth

If the value of b <1 ----> then is a exponential decay

Verify each case

case a) we have

`y=((5)/(4))^x`

`b=(5)/(4)`

b> 1

therefore

The function represent exponential growth

case b) we have

`y=(4)^(-x)`

`b=(1)/(4)`

b< 1

therefore

The function represent exponential decay

case c) we have

`y=5^x`

`b=5`

b> 1

therefore

The function represent exponential growth

case d) we have

`y=((4)/(5))^x`

`b=(4)/(5)`

b< 1

therefore

The function represent exponential decay