Chapter 8.5, Problem 55STP

a.

To determine

To make a table to show the expected length of Audrey’s hair in each of first 4 years

Answer to Problem 55STP

The table for the expected length of Audrey’s hair in each of first 4 years is

Year	Length
In 1st year	10 inches
In 2nd year	13 inches
In 3rd year	16 inches
In 4th year	19 inches

Explanation of Solution

Given information:

Audrey’s hair is 7 inches long and is expected to grow at an average rate of 3 inches per year

Audrey’s hair grow 3 inches per year so,

After 1 year its length will be = $7+3=10$ inches

After 2 years its length will be = $10+3=13$ inches

After 3 years its length will be = $13+3=16$ inches

After 4 years its length will be = $16+3=19$ inches

The table for the length Audrey’s hair can be obtained as,

Year	Length
In 1st year	10 inches
In 2nd year	13 inches
In 3rd year	16 inches
In 4th year	19 inches

Therefore, the table is for length of Audrey’s hair of first 4 years is obtained

b.

To determine

To write the function that can be used to determine the length of Audrey’s hair after each year

Answer to Problem 55STP

The function that can be used to determine the length of Audrey’s hair after each year is $l=7+3y$

Explanation of Solution

Given information:

Audrey’s hair is 7 inches long and is expected to grow at an average rate of 3 inches per year

Since Audrey’s hair is 7 inches long and expected to grow 3 inches every year so its expression can be written as,

  $l=7+3y$

Here, $l$ is the length of the hair and $y$ is the year

Therefore, the obtained function is $l=7+3y$

c.

To determine

To determine the length of Audrey’s hair after 9 years if she does not get a hair cut

Answer to Problem 55STP

The length of Audrey’s hair after 9 years will be 34 inches

Explanation of Solution

Given information:

Audrey’s hair is 7 inches long and is expected to grow at an average rate of 3 inches per year

Each year Audrey’s hair is expected to grow 3 inches so length of her hair after 9 years can be obtained as,

After 1 year its length will be = $7+3=10$ inches

After 2 years its length will be = $10+3=13$ inches

After 3 years its length will be = $13+3=16$ inches

After 4 years its length will be = $16+3=19$ inches

After 5 years its length will be = $19+3=22$ inches

After 6 years its length will be = $22+3=25$ inches

After 7 years its length will be = $25+3=28$ inches

After 8 years its length will be = $28+3=31$ inches

After 9 years its length will be = $31+3=34$ inches

Therefore, the length of Audrey’s hair after 9 years will be 34 inches