Question

Which equation represents exponential growth? plz help me

y = (0.25)^x
y = (7)^x
y = 1/3 (0.1)^x
y = (2/3)^x

Answer 1

B

Explanation:

Exponential function
`y=a\cdot b^x` represents

• exponential growth if
  `b>1;`
• exponential decay if
  `0<b<1.`

Consider all options:

A. In the exponential function
`y=(0.25)^x,`

`b=0.25<1,`

so it represents exponential decay.

B. In the exponential function
`y=7^x,`

`b=7>1,`

so it represents exponential growth.

C. In the exponential function
`y=(1)/(3)(0.1)^x,`

`b=0.1<1,`

so it represents exponential decay.

D. In the exponential function
`y=\left((2)/(3)\right)^x,`

`b=(2)/(3)<1,`

so it represents exponential decay.