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Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was 160 meters away. After 3 seconds of driving, she was 85 meters away from the safe zone.
Let
y represent the distance (in meters) from the safe zone after
x seconds.
Complete the equation for the relationship between the distance and number of seconds.

y=

Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was $160$ meters away. After $3$ seconds of driving, she was $85$ meters away from the safe zone. $\newline$ Let $y$ represent the distance (in meters) from the safe zone after $x$ seconds. $\newline$ Complete the equation for the relationship between the distance and number of seconds. $\newline$ $y=\square$

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Write exponential functions: word problems

Full solution

Q. Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was

160

meters away. After

3

seconds of driving, she was

85

meters away from the safe zone.

\newline

Let

y

represent the distance (in meters) from the safe zone after

x

seconds.

\newline

Complete the equation for the relationship between the distance and number of seconds.

\newline

y=\square

Initial Distance Determination: Determine the initial distance from the safe zone. $\newline$ Kayden starts at a distance of $160$ meters from the safe zone.
Distance Covered Calculation: Determine the distance covered in $3$ seconds. $\newline$ After $3$ seconds, Kayden is $85$ meters away from the safe zone. This means she covered $160 - 85 = 75$ meters in $3$ seconds.
Speed Calculation: Calculate the speed of Kayden's car. Speed is the distance covered divided by the time taken. Kayden covered $75$ meters in $3$ seconds, so her speed is $\frac{75 \text{ meters}}{3 \text{ seconds}} = 25 \text{ meters per second}.$
Equation Writing: Write the equation for the distance from the safe zone after $x$ seconds. $\newline$ Since Kayden is moving at a constant speed, the distance from the safe zone decreases linearly over time. The equation relating the distance from the safe zone, $y$ , after $x$ seconds is $y = \text{initial distance} - (\text{speed} \times \text{time})$ . Using the values we have, the equation becomes $y = 160 - 25x$ .

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