Question

The average low temperature by month in Nashville is represented by the function (m) = -1.4m^2 + 17, where m is the month. What is the average rate of change from March to August?

A) -20.8
B) -18.6
C) -12.6
D) -8.4

Answer 1

The average rate of change from March to August in the average low temperature in Nashville can be found by calculating the difference between the temperatures in these months.

Step-by-step explanation:

The average rate of change from March to August can be found by calculating the difference in the average low temperatures between these months. The function (m) = -1.4m^2 + 17 represents the average low temperature in Nashville by month, where m is the month. To find the average low temperature in March, substitute m = 3 into the function and simplify. Similarly, substitute m = 8 to find the average low temperature in August. Finally, calculate the difference between these two temperatures.

Using the given function, the average low temperature in March is:

(3) = -1.4(3)^2 + 17

= -1.4(9) + 17

= -12.6 + 17

= 4.4

The average low temperature in August is:

(8) = -1.4(8)^2 + 17

= -1.4(64) + 17

= -89.6 + 17

= -72.6

To find the average rate of change, calculate the difference between the temperatures:

Average rate of change = Average low temperature in August - Average low temperature in March

= -72.6 - 4.4

= -77