Answer
The rate of change of the temperature after an hour is $-\frac{5}{6}^oF/min$, or the turkey loses $\frac{5}{6}^oF$ every minute after an hour.
Work Step by Step
We would call the function from the graph $T=f(t)$
To estimaate the slope of the tangent at $t=60$, we would
- pick 2 close points from $t=60$, which are $t=30$ and $t=90$ and figure out the values of $f(30)$ and $f(90)$
- Find the value of $\frac{f(90)-f(30)}{90-30}$. The result is the estimated slope of the tangent.
From the graph, we see that $f(30)=150$ and $f(90)=100$
Therefore, the slope of the tangent is $$m=\frac{f(90)-f(30)}{90-30}=\frac{100-150}{60}=-\frac{5}{6}$$
The unit here is $^oF/min$.
In conclusion, the rate of change of the temperature after an hour is $-\frac{5}{6}^oF/min$, or the turkey loses $\frac{5}{6}^oF$ every minute after an hour.
