Chapter 3.2, Problem 44PPS

(a)

To determine

Find the zero of this function.

Answer to Problem 44PPS

  $t=8$ Minutes

Explanation of Solution

Given:

Chemical hair straightening makes curly hair straight and smooth. The percent of the process left to complete is modeled by $p=-12.5t+100$ , where $t$ is the time in minutes that the solution is left on the hair, and $p$ represents the percent of process left to complete.

Concept Used:

Calculation:

Find the zero of this function:

  $\begin{array}{l}p=-12.5t+100\\ 0=-12.5t+100[\text{plug}\text{in}\text{p = 0}]\\ 0+12.5t=-12.5t+12.5t+100\text{[}\text{Add}12.5t\text{to}\text{both}\text{sides}\text{]}\\ 12.5t=100\\ \frac{12.5t}{12.5}=\frac{100}{12.5}[\text{Divide}\text{each}\text{side}\text{by}12.5]\\ t=8\end{array}$

Thus, zero of the function t = 8 minutes.

(b)

To determine

Graph the situation.

Explanation of Solution

Given:

Chemical hair straightening makes curly hair straight and smooth. The percent of the process left to complete is modeled by $p=-12.5t+100$ , where $t$ is the time in minutes that the solution is left on the hair, and $p$ represents the percent of process left to complete.

Concept Used:

To graph the situation, Make a table of the equation $p=-12.5t+100$ by taking some random value t and calculate the corresponding value of p. Plot the points on the grid and join the points to make a linear graph.

Calculation:

Make a graph of this function.

Table	$p=-12.5t+100$
$t$ $p=-12.5t+100$ $p$ $(t,p)$ 0 $\begin{array}{l}p=-12.5·0+100\\ p=100\end{array}$ $100$ $(0,100)$ 8 $\begin{array}{l}p=-12.5·8+100\\ p=-100+100=0\end{array}$ $0$ $(8,0)$

(c)

To determine

Explain what the zero represent in this contest.

Answer to Problem 44PPS

After 8 minutes the total Chemical hair straightening process will complete.

Explanation of Solution

Given:

Chemical hair straightening makes curly hair straight and smooth. The percent of the process left to complete is modeled by $p=-12.5t+100$ , where $t$ is the time in minutes that the solution is left on the hair, and $p$ represents the percent of process left to complete.

Concept Used:

After 8 minutes the total Chemical hair straightening process will complete.

Thus, after 8 minutes the total Chemical hair straightening process will complete.

(d)

To determine

State the possible domain and range of this function.

Answer to Problem 44PPS

Domain: $-\infty <t<\infty \text{or}(-\infty ,\infty )$ and Range: $-\infty <p<\infty \text{or}(-\infty ,\infty )$

Explanation of Solution

Given:

Chemical hair straightening makes curly hair straight and smooth. The percent of the process left to complete is modeled by $p=-12.5t+100$ , where $t$ is the time in minutes that the solution is left on the hair, and $p$ represents the percent of process left to complete.

Concept Used:

Domain and range both are all real numbers.

Calculation:

Domain: $-\infty <t<\infty \text{or}(-\infty ,\infty )$

Range: $-\infty <p<\infty \text{or}(-\infty ,\infty )$

Thus, Domain: $-\infty <t<\infty \text{or}(-\infty ,\infty )$ and Range: $-\infty <p<\infty \text{or}(-\infty ,\infty )$