Chapter 1.1, Problem 53E

Funding for NASA: 1958-1966 The percentage of the U.S. federal budget allocated to NASA from 1958 to 1966 can be approximated by

$p\left(t\right)=\frac{4.5}{{1.07}^{{\left(t-8\right)}^2}}$ percentage points ${\left(t\text{is}\text{time}\text{in}\text{years}\text{since}\text{1958}\right)}^{12}$. The following graph shows the data with the model:

a. Find an appropriate domain of p. Is $t\ge 0$ an approximate domain? Why or why not?

b. Compute $p\left(5\right)$ accurate to one decimal place. What does the answer say about the budget allocation to NASA?

c. At which of the following values oft is $p\left(t\right)$ increasingmost rapidly: 0, 3, 5, 8? Interpret your answer.