Question

The function d = 16t2 models the distance d, in feet, that an object falls in t seconds. Find the inverse function and use the inverse function

o estimate the time it takes an object to fall 100 feet. (1 point)

Answer 1

`t = (1)/(4)\sqrt d`

Time to reach 100ft is 2.5 seconds

Explanation:

Given

`d = 16t^2`

Solving (a): Determine the inverse function

`d = 16t^2`

Swap the positions of d and t

`t = 16d^2`

Make d the subject

`(t)/(16) = d^2`

Take positive square root of both sides

`\sqrt{(t)/(16)} = d`

`d = \sqrt{(t)/(16)}`

`d = (1)/(4)\sqrt t`

Swap the positions of d and t

`t = (1)/(4)\sqrt d` --- The inverse function

Solving (b): Find t when d =100

Substitute 100 for d in
`t = (1)/(4)\sqrt d`

`t = (1)/(4)\sqrt {100`

`t = (1)/(4)* 10`

`t = (1* 10)/(4)`

`t = (10)/(4)`

`t = 2.5`