Q. 76 - Calculus

Question

The following graph describes the temperature T(t) of a yam in an oven, where temperature T is measured in degrees Fahrenheit and time t is measured in minutes:

(a) Use the graph to approximate the temperature of the yam when it is first put in the oven.

(b) Use the graph to approximate $\underset{t\to \infty }{\lim }T\left(t\right).$

(c) What is the temperature of the oven, and why?

Step-by-Step Solution

Answer

Part (a) The temperature of the yam when it is first put in the oven is $50°\mathrm{F}.$

Part (b) After approximating the value of the limit $\underset{t\to \infty }{\lim }T\left(t\right)=350.$

Part (c) The temperature of the oven is $350°\mathrm{F}.$ because the temperature of yam doesn't increase as the time increase.

Part (a) Step 1. Given Information.

The given graph is

Part (a) Step 2. Using the graph to approximate the temperature of the yam when it is first put in the oven.

From the graph, we can depict that at $t=0,$ the temperature is $50°F.$

Therefore, the temperature of the yam when it is first put in the oven is  $\mathbf{50}\mathbf{°}\mathbf{F}\mathbf{.}$

Part (b) Step 1. Using the graph to approximate lim t → ∞ T ( t ) .

From the graph, we can depict that when $t\to \infty$, the corresponding functional value remains constant at $350.$

Therefore, the value of the limit $\underset{t\to \infty }{\lim }T\left(t\right)=350.$

Part (c) Step 1. Find the temperature of the oven.

The temperature of the oven is $350°\mathrm{F}$ because the temperature of yam doesn't increase as the time increase.