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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)

User Hellion
by
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1 Answer

6 votes

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

User Benjamin Morrison
by
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