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 o…

Question

asked Apr 22, 2022 116k views

1 Answer

Benjamin Morrison · Answer 1 · 2022-04-28T10:27:52+0000

Answer:

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

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