2. At the beginning of a trip, the odometer on a car reads 30,680 and the
car has a full tank of gas. At the end of the trip, the odometer reads
30,970. It takes 20 gallons of gas to refill the tank.
a. What is the average rate of change of the number of miles with respect
to the number of gallons?
3. The total number of words M(t) that a person can memorize in time t, in
minutes, is shown in the following table
t
8 16 24 32 36
M(t) 10 20 25 25 25
a. Find the average rate of change of M as t changes from 8 to 16.
b. Find the average rate of change of M as t changes from 16 to 24.
c. Find the average rate of change of M as t changes from 24 to 32.

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MrRoyal MrRoyal · Answer 1 · 2022-06-21T19:38:49+02:00

The average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The given parameters can be represented as:

M(0) = 30680

M(20) = 30970

The average rate of change is calculated as:

M'(t) = (M(20) - M(0))/(20 - 0)

This gives

M'(t) = (30970 - 30680)/(20 - 0)

M'(t) = 14.5

Hence, the average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The average rate of change of M as t changes from 8 to 16.

This is calculated using

M'(t) = (M(16) - M(8))/(16 - 8)

M'(t) = (20 - 10)/(16 - 8)

M'(t) = 1.25

The average rate of change of M as t changes from 16 to 24.

This is calculated using

M'(t) = (M(24) - M(16))/(24 - 16)

M'(t) = (25 - 20)/(24 - 16)

M'(t) = 0.625

The average rate of change of M as t changes from 24 to 32.

This is calculated using

M'(t) = (M(32) - M(24))/(32 - 24)

M'(t) = (25 - 25)/(32 - 24)

M'(t) = 0