a.
Lauren was 10 miles away from her house when he started.
Since the expression for Lauren's distance from her house, d = -2t + 10, to determine the number of miles away from his house that Lauren starts, we input t = 0, since this is the time Lauren starts walking.
So, with t = 0, d = -2t + 10
= -2(0) + 10
= 0 + 10
= 10 miles.
So, Lauren was 10 miles away from her house when he started.
b.
Lauren was moving at a rate of -2 mph towards her house.
To find how fast Lauren was moving towards her house, we differentiate d with respect to t.
So, dd/dt = d(-2t + 10)/dt
= d(-2t)/dt + d(10)/dt
= -2 + 0
= -2 mph
So, Lauren was moving at a rate of -2 mph towards her house.
c.
The rate is negative because her distance towards her house is decreasing
The rate is negative because her distance towards her house is decreasing since she is moving towards her house.
d.
Lauren is 2 miles away from her house after 4 hours
To find this, we input t = 4 into the equation for d.
So, d = -2t + 10
= -2(4) + 10
= -8 + 10
= 2 miles.
So, Lauren is 2 miles away from her house after 4 hours
Learn more about distance travelled here:
brainly.com/question/17997145
