Linear Models

How many inches did she improve over the first 60 days?

How many inches did she improve over the first 120 days?

How many inches did she improve over the first 180 days?

2 inches

4 inches

6 inches

How did you determine your answers for questions 1 – 3?

5. Using t for the number of training days, write an expression that represents the number of inches she improves over t days of training.

Discuss with your partner

t .30

6. How many inches could Keanani pole vault at the beginning of 180 days?

7. How many inches could she pole vault after 90 days of training?

8. How many inches could she pole vault after 150 days of training?

138 inches

141 inches

143 inches

9. How did you determine your answers to questions 6, 7, and 8?

10. Using your expression from question 5, find a symbolic representation for the height Keanani can pole vault, H(t), t days after she began training.

Discuss with your partner

𝐻 (𝑡 )= 𝑡30

+138

12. What does the y-intercept represent in context?

13. What is the rate of change of this function and what does it represent in context?

14. What is another name for the rate of change of a linear function?

The height she could jump when she started training, which is 138 inches

She can jump 1 inch every 30 days

slope

15. If Keanani continues practicing and continues to improve at the same rate, how high will she be able to pole vault after 240 days?

16. How high can she pole vault after 195 days?

146 inches

144.5 inches

17. How long will it take her to reach 13 ft?

18. How long will it take her to reach 13 ½ feet?

540 days

720 days

19. Explain the difference in how you answered questions 15 and 16 to questions 17 and 18.

Discuss with your partner

20. The height Alexi can pole vault after t days of training, A(t), is also linear. What part(s) of the symbolic representation H(t), the slope and/or the y-intercept, must you change in order to symbolically represent A(t)?

21. Find the symbolic representation for A(t)

The slope

𝐴 (𝑡 )= 𝑡20

=138