Question

The amount of money, M, in dollars, in a piggy bank after 1 days is given by M - 2t ^ 3 + 2t + 10 Determine the average rate of change of the amount of money in the piggy bank from day 1 today 3. [C 5]

Answer 1

The average rate of change of the money in the piggy bank from day 1 to day 3 is found by subtracting the amount on day 1 from the amount on day 3 and dividing by the time interval, resulting in -27 dollars per day.

Step-by-step explanation:

To determine the average rate of change of the amount of money in the piggy bank from day 1 to day 3, we need to use the equation M = -2t³ + 2t + 10, where M stands for the amount of money and t represents the number of days. To calculate the average rate of change, subtract the initial amount of money from the final amount of money, and divide by the change in days:

1. Calculate the amount of money on day 1: M1 = -2(1)³ + 2(1) + 10 = 10.
2. Calculate the amount of money on day 3: M3 = -2(3)³ + 2(3) + 10 = -44.
3. Compute the average rate of change: ((-44) - 10) / (3 - 1) = -27.

The average rate of change of the amount of money in the piggy bank from day 1 to day 3 is '-27 dollars per day.