Question

Patrick made tortilla soup in his slow cooker and has turned the heat off to allow the soup to cool slightly before consuming. The temperature, in degrees Fahrenheit, of the soup x minutes after the heat was turned off is represented by the function below.
T(x) = 15 + 155e-0.02x

What is the approximate average rate of change over the interval [10, 30]?

A.
-6.05 degrees per minute
B.
-1.05 degrees per minute
C.
-41.84 degrees per minute
D.
-2.09 degrees per minute

Answer 1

9514 1404 393

Answer:

  D.  -2.09 degrees per minute

Step-by-step explanation:

The average rate of change is the change in temperature divided by the change in time:

  m = (T(30) -T(10))/(30 -10)

  = ((15 +155 e^(-30·0.02)) -(15 +155 e^(-10·0.02))/20

  = (155/20)(e^-0.6 -e^-0.2) ≈ -2.09 . . . degrees per minute