Answer
$ H'(t)=3.5t+65\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,
$(0,65) \quad$ 65 billion in year 1990 ($t=0$)
$(10,100) \quad$ 100 billion in year 2000 ($t=10$)
$m=\displaystyle \frac{100-65}{10-0}=3.5$
Point slope form: $\left[\begin{array}{l}
y-y_{1}=m(x-x_{1})\\
y-65=3.5(x-0)\\
y=3.5x+65
\end{array}\right]$
$ H'(t)=3.5t+65\quad$ (billion dollars per year.)
