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Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove to get to the safe zone at 24 meters per second. After 4 seconds of driving, she was 70 meters away from the safe zone

Respuesta :

frika

Answer:

[tex]D(t)=-24t+166[/tex]

Step-by-step explanation:

Let

D(t) = the distance to the safe zone (measured in meters)

t = time (measured in seconds)

Given:

Rachel's rate = 24 meters per second

At [tex]t_1=4[/tex] seconds [tex]D(t_1)=70[/tex] meters

Find: D(t)

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative.

Hence, the function expression is

[tex]D(t)=-24t+b[/tex]

To find b, substitute [tex]t_1=4[/tex] and  [tex]D(t_1)=70:[/tex]

[tex]70=-24\cdot 4+b\\ \\70=-96+b\\ \\b=70+96\\ \\b=166[/tex]

So,

[tex]D(t)=-24t+166[/tex]

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