Chapter 1.1, Problem 53E

(a)

To determine

The appropriate domain for $p$, which is the percentage of U.S. federal budget allocated to NASA from $1958$ to $1966$ and it is approximated by $p\left(t\right)=\frac{4.5}{{1.07}^{{\left(t-8\right)}^2}}$

Percentage points. The following graph shows the data with the model

(b)

To determine

The value of $p\left(5\right)$ up to one decimal place. Also determine what the answer say about the budget allocation to NASA. Percentage of U.S. federal budget allocated to NASA from $1958$ to $1966$ and it is approximated by $p\left(t\right)=\frac{4.5}{{1.07}^{{\left(t-8\right)}^2}}$

Percentage points. The following graph shows the data with the model. Whether $t\ge 0$ is an appropriate domain.

(c)

To determine

The approximate value of $t$ for which $p\left(t\right)$ is increases most rapidly in the following values: $0,3,5$ or $8$ for the following graph. The following graph shows the data with the model