AFDA – Unit 7: Exponential and Logarithmic Functions
Day 5 HW: Exponential and Logarithmic Regressions
Name: _________________
Block: _____ Date:_______
Directions: Answer the following questions. Round to three decimals if necessary.
1. Rabbits were accidentally introduced to an island where their population is growing
rapidly. Biologists studying the rabbits have periodically recorded their population
since they were introduced to the island. The data they took is shown below.
Years Since Introduction, x
Population of Rabbits, Population of
Rabbits, y
2
75
5
7
11
15
100 112 205 290
a. Enter the data in your calculator, look at the scatterplot, and describe/draw
any patterns you see (think function + behaviors).
b. What is the equation of the regression line of best fit?
c. What is the 𝑟 2 value? What does this mean?
d. What is the rabbit population in year 9? Is this interpolation or extrapolation?
THERE IS A BACK!
2. During prolonged cold in northern latitudes, thick ice will grow on lakes. A particular
lake in Ladysmith, Wisconsin has its ice thickness measured every day after the
temperature fell below zero. The data is shown in the table below.
Days Below Freezing,
x
Ice Thickness (in
inches), y
6
9
14
20
27
32
55
0.8 1.7 3.5 4.0 5.2 5.5 7.2
a. Enter the data in your calculator, look at the scatterplot, and describe/draw
any patterns you see (think function + behaviors).
b. What is the equation of the regression line of best fit?
c. What is the 𝑟 2 value? What does this mean?
d. What is the ice thickness after 70 days below freezing? Is this interpolation or
extrapolation?