# C TateSullivan Unit Test Part 2 Math

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Name: Caitlin Tate-Sullivan
Date: 5/23/15
Graded Assignment
Unit Test, Part 2: More Math Models
Answer the questions. When you have finished, submit this assignment to your teacher by the due date for full credit.
(10 points)
1. There are 400 rice weevils at the beginning of an insect study. The population is expected to grow at a rate of 150% each week.
A. Write and simplify a formula that can be used to predict the rice weevil population for any week after the beginning of the study.
B. Use the formula to predict the rice weevil population 10 weeks after the beginning of the study. Show your work.
C. Use the formula to predict when the rice weevil population will reach 1,000,000,000. Show your work.
Answer:
400(1+150/100)^10 = 400*2.5^10 = 3,814,697
1,000,000,000 = 400*2.5^t
2.5^t = 2,500,000
T = log^2,500,000/log^2.5 = 16.0776 ==> 16 weeks

(8 points)
2. The graph shows the vertical displacement y, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds, x.

A. What is the weight’s maximum displacement?
B. From its resting position, how long does it take the weight to bounce one direction, then the other, and then return to its resting position?
C. What is the graph’s frequency and what does it indicate in this situation?
D. How is the weight moving during the time period x = 6 to x = 7.5?
Answer:
A. 20
B.

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