Chapter 1.1, Problem 54E

Funding for NASA: 1966-2015 The percentage of the U.S. federal budget allocated to NASA from 1966 to 2015 can be approximated by $p\left(t\right)=0.03+\frac{5}{t^{0.6}}$ percentage points $\left(t\ge 1\right)$

$\left(t\text{is}\text{time}\text{in}\text{years}\text{since}\text{1965}\right){.}^{13}$

The following graph shows the data with the model:

a. Find an appropriate domain of p. Is $\left[0,50\right]$ an appropriate domain? Why or why not?

b. Compute $p\left(40\right)$ accurate to two decimal places. What does the answer say about the budget allocation to NASA?

c. If the model is extrapolated to larger and larger values of t, what does it suggest about long-term financing of NASA?