Answer
$H'(t)=9t+100 \quad$(billion dollars per year)
Work Step by Step
The instantaneous rate of change of $H(t)$ is $H'(t)$
We approximate $H'(t)=mx+b,$
where m is the slope between the two given data points,
$(0,100) \quad$ $100$ billion in year $2000$ ($t=0$)
$(10,190) \quad$ $190$ billion in year $2010$ ($t=10$)
$m=\displaystyle \frac{190-100}{10-0}=9$
Point-slope form: $\left[\begin{array}{l}
y-y_{1}=m(x-x_{1})\\
y-100=9(x-0)\\
y=9x+100
\end{array}\right]$
$H'(t)=9t+100 \quad$(billion dollars per year)
