Chapter PS, Problem 9.1P

a.

To determine

To find: A piecewise function L .

Answer to Problem 9.1P

  $L=\{\begin{array}{ccc}3t& \text{,if}& 0<t\le 10\\ t& \text{,if}& 10<t\le 15\\ \frac{1}{3}t& \text{,if}& 15<t\le 24\end{array}$

Explanation of Solution

Given: For first 10 hours of play, Issac leveled 3 times each hours. For next 5 hours of play, only leveled once an hour. For the final nine hours of play, Isaac leveled once evry three hours.

To make piecewise function of above info where L represent level of time t

For first 10 hours of play, Issac leveled 3 times each hours.

  $L=3t,0<t\le 10$

For next 5 hours of play, only leveled once an hour.

  $L=t,10<t\le 15$

For the final nine hours of play, Isaac leveled once every three hours

  $L=\frac{1}{3}t,15<t\le 24$

So, piecewise function is

  $L=\{\begin{array}{ccc}3t& \text{,if}& 0<t\le 10\\ t& \text{,if}& 10<t\le 15\\ \frac{1}{3}t& \text{,if}& 15<t\le 24\end{array}$

b.

To determine

To find: A level when after 18 hours of play .

Answer to Problem 9.1P

  $6$

Explanation of Solution

Given: For first 10 hours of play, Issac leveled 3 times each hours. For next 5 hours of play, only leveled once an hour. For the final nine hours of play, Isaac leveled once evry three hours.

After 18 hours at what level.

Take function for $t=18$

  $L=\{\begin{array}{ccc}3t& \text{,if}& 0<t\le 10\\ t& \text{,if}& 10<t\le 15\\ \frac{1}{3}t& \text{,if}& 15<t\le 24\end{array}$

So, $L=\frac{1}{3}t$

Put $t=18$ into above function.

  $L=\frac{1}{3}\times 18=6$

At leveled 6.