AnswersFL-1200330-Algebra 2 CRModeling with Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Equations Answers

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1
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The data show that the population of lily pads has growth rate.

A
a steady
B
an increasing
C
a decreasing
2
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function would be most suitable to model these data.

A
A logarithmic
B
An exponential
C
A linear
D
A quadratic
3

Type the data that you collected (shown right) into the regression calculator. Be sure to choose a good window setting! The general form of an exponential function is y = abx. Use the regression calculator to find the values of a and b for the water lily population growth. Round to the nearest thousandth.

Answers:
a =:3.915
and b =:1.106
7

The slider only goes up to day 30, but this pond can hold up to 400 water lilies. Estimate the day that the pond will be full. Day

Answer:

32

8

The graph to the right shows what you should have gotten on the regression calculator. Check all statements below that accurately describe the regression equation.

A
Some points do not lie on the regression curve, so it is not a good model.
B
Most points lie on or near the regression curve, so it is a good model.
C
The equation can be used to analyze the population growth, and to estimate values outside of what was collected.
9

Which two equations below could you solve to find D, the number of days it takes the water lily population to double?

A
2 = 3.915(1.106)D
B
7.830 = 3.915(1.106)D
C
7.830 = 3.915(2)D
D
2 = 1.106D
10

Try a few examples to verify that the doubling time is indeed 7 days.

Answers:
Day 0::4
Day 7::8
Day 10::10
Day 17::22
11

The pond can hold 400 water lilies. By what day will the pond be full? Write and solve an equation.The pond will be full by the end of day .

Answer:

46

12

Which solution method did you use?

A
Logarithms
B
Graphing y = 3.915(1.106)x and tracing
C
Graphing y = 3.915(1.106)x and y = 400, then finding the x-value of the intersection
13

Solve either of the correct equations using any method. Round to the nearest whole number.D = days

Answer:

7

14

By the 46th day, there are 400 water lilies in the pond. The estimate you made

A
close to 46 (or exactly right) because it was estimated well.
B
too low because the quick exponential growth was not accounted for.
C
too high because the exponential growth was overestimated.
15

Did the water lilies double?

Answers:
Selection 1:Yes
Selection 2:Approximately

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Modeling with Exponential and Logarithmic Equations