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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)


Sagot :

Answer:

[tex]t = \frac{1}{4}\sqrt d[/tex]

Time to reach 100ft is 2.5 seconds

Step-by-step explanation:

Given

[tex]d = 16t^2[/tex]

Solving (a): Determine the inverse function

[tex]d = 16t^2[/tex]

Swap the positions of d and t

[tex]t = 16d^2[/tex]

Make d the subject

[tex]\frac{t}{16} = d^2[/tex]

Take positive square root of both sides

[tex]\sqrt{\frac{t}{16}} = d[/tex]

[tex]d = \sqrt{\frac{t}{16}}[/tex]

[tex]d = \frac{1}{4}\sqrt t[/tex]

Swap the positions of d and t

[tex]t = \frac{1}{4}\sqrt d[/tex] --- The inverse function

Solving (b): Find t when d =100

Substitute 100 for d in [tex]t = \frac{1}{4}\sqrt d[/tex]

[tex]t = \frac{1}{4}\sqrt {100[/tex]

[tex]t = \frac{1}{4}* 10[/tex]

[tex]t = \frac{1* 10}{4}[/tex]

[tex]t = \frac{10}{4}[/tex]

[tex]t = 2.5[/tex]

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