Chapter 1.1, Problem 14E

Reminder Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

A Roast is taken from the refrigerator (where it had been for several days) and placed immediately in a preheated oven to cook. The temperature $R=R\left(t\right)$ of the roast $t$ minutes after being placed in the oven is given by

$R=325-280e^{-0.005t}\text{degrees}\text{Fahrenheit}$

a. What is the temperature of the refrigerator?

b. Express the temperature of the roast $30$ minutes after being put in the oven in functional notation, and then calculate its value.

c. By how much did the temperature of the roast increase during the first 10 minutes of cooking?

d. By how much did the temperature of the roast increase from the first hour to 10 minutes after the first hour of cooking?