Chapter 1.1, Problem 41PPSE

Solution

To find: The height of the person after $5$ years.

The height of the person after five year is $\text{6}\text{ft}\text{9}\text{inches}\text{.}$

Given information:

The present height of the person is $5\text{ft }6\text{in}$.

Growth rate is $3$ inches per year.

Concept used:

The rule of the pattern here is to get the following number add $3$ to the preceding number.

  $12\text{in}=1\text{ft}$

Calculations:

Change $5\text{ft }6\text{in}$ into inches.

  $\begin{array}{c}5\text{ft }6\text{in}=12\times 5+6\\ =66\text{ in}\end{array}$

When he was 15 years, the height was $66\text{in}$ .

So, the point $\left(15,66\right)$ and the growing with 3 in per year. So, the slope is 3.

Let be $y$ inches the height of the person after $x$ years. $5\text{ft }6\text{in}$

According to the equation,

  $\begin{array}{c}y-66=3\left(x-15\right)\\ y=3x-45+66\\ y=3x+21\end{array}$

Put $x=20$ and the height is,

  $\begin{array}{c}y=3\left(20\right)+21\\ y=60+21\\ y=81\end{array}$

Now change 81 inches to ft.

  $81\text{ in}=6\text{ft 9}\text{in}$

Thus, the height of a person in 20 years will be 6 ft 9 in.

So, the prediction was right.