1. Functions-Part 3

2. Paul went to get a haircut
Paul went to get a haircut. When he got home, he looked in the mirror and screamed, “It’s too short!” He decided not to get his hair cut again for a long time. In the meantime, he decided to measure how fast his hair grew. Below is a table that shows the length of Paul’s hair (in centimeters) as he measured it each month.

3. How long was Paul’s hair after the haircut
How long was Paul’s hair after the haircut? Why is it easy to calculate its length? How long will Paul’s hair be after one year if it keeps growing and he does not get a haircut?

4. Draw a graph showing how Paul’s hair grows after one year if he does not get a haircut.

5. Describe the shape of the graph
Describe the shape of the graph. If Paul’s hair is 10 cm long at some point, how long will it be one month later?

6. If you know the length of Paul’s hair in the current month, you can use it to find his hair length for the next month. Write a formula using NEXT and CURRENT.

7. You knew that the length of Paul’s hair at the beginning was 2 cm
You knew that the length of Paul’s hair at the beginning was 2 cm. That’s why it is possible to make a direct formula for Paul’s hair growth: L = T What does the letter L stand for? The letter T? Explain the numbers in the formula. Sacha’s hair is 20 cm long and grows at a constant rate of 1.4 cm a month. Write a direct formula with L and T to describe the growth of Sacha’s hair.

8. Suppose you decided not to cut one fingernail for several months, and the nail grew at a constant rate. The table shows the lengths of a nail in millimeters at the beginning and after four months. How much did this nail grow every month? Predict what the graph that fits the data in the table looks like. If you cannot predict its shape, think of some points you might use to draw the graph. Write a direct formula for fingernail growth using L for length (in millimeters) and T for time (in months).