Question

Which of the following exponential function me goes through the points (1,20) and (2,80)

Answer 1

`f(x)=5(4^x)`

Explanation:

Let
`y=ab^x` be the equation of the exponential function.

This exponential function goes through (1,20).

We put x=1 and y=20 into the above equation to get:

`20=ab^1`

`20=ab`.....eqn (`1)

This exponential function again goes through (2,80).

We put x=2 and y=80 into the above equation to get:

`80=ab^2`.....eqn (`2)

Divide equation (2) by equation (1)

`(80)/(20)=(ab^2)/(ab)`

`\implies 4=b`

Put b=4 in equation 1.

`20=4a`

`\implies a=5`

The required exponential function is
`y=5(4^x)` or
`f(x)=5(4^x)`