
Differentiate both sides with respect to

:

When

, you have

For part (b), we now assume that

and

are functions of an independent variable, which we'll call

(for time). Now differentiating both sides with respect to

, we have

where the chain rule is used on the right side. We're told that

is decreasing at a constant rate of 0.1 units/second, which translates to

. So when

, you have



where the unit is again units/second.
Answer:
If k is an integer, the number of toy cars Ken might have can be expressed as the interval
0 ≤ k < 25
It took 2 hours and 15 minutes to catch up
they have driven about 225 kilometers at this point.