Answer
a. $200^{\mathrm{o}}$
b. graph: $\approx 120^{\mathrm{o}}$, calculator: $\approx 119^{\mathrm{o}}$
c. $70^{\mathrm{o}}$, room also at $70^{\mathrm{o}}$
Work Step by Step
a.
As the cup is taken out of the microwave, t=0.
The graph shows that at t=0, T=$200^{\mathrm{o}}$,
( the temperature of the coffee was $200^{\mathrm{o}}$)
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b.
After 20 minutes, t=20, reading the graph,
we estimate that T=$120^{\mathrm{o}}$, or that
the temperature of the coffee was about $120^{\mathrm{o}}$.
Using a calculator,
$T=70+130e^{-0.04855\cdot 20}\approx 119.2$
( the temperature is about $119^{\mathrm{o}}$).
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c.
We recognize a horizontal asymptote, so
T will approach, but not reach $70^{\mathrm{o}}$
The coffee will cool to about $70^{\mathrm{o}}$.
The coffee will eventually cool to room temperature,
so the temperature of the room is $70^{\mathrm{o}}$.
