Answer
$ a.\quad 200^{\mathrm{o}}$
$ b.\quad $ Graph estimate: about $120^{\mathrm{o}}$, Calculator: about $119^{\mathrm{o}}$
$ c.\quad 70^{\mathrm{o}}$, which is the room temperature
Work Step by Step
$ a.$
At time t=0, the corresponding point on the graph is (0,200), meaning that the temperature of the coffee was $200^{\mathrm{o}}.$
$ b.$
At t=20 minutes, the corresponding point on the graph is (20,120); the temperature of the coffee was about $120^{\mathrm{o}}.$
Using a calculator,
$ T=70+130e^{-0.04855(20)}\approx 119.2315$
the temperature is about $119^{\mathrm{o}}.$
$\mathrm{c}$.
The asymptote of the graph is $ T\approx 70$, meaning that the coffee will cool to about $70^{\mathrm{o}}$
(and reach equilibrium with the room temperature.)
The room temperature is about $70^{\mathrm{o}}$.
