Question

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

Answer 1

`D(t)=-24t+166`

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
`t_1=4` seconds
`D(t_1)=70` 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

`D(t)=-24t+b`

To find b, substitute
`t_1=4` and
`D(t_1)=70:`

`70=-24\cdot 4+b\\ \\70=-96+b\\ \\b=70+96\\ \\b=166`

So,

`D(t)=-24t+166`