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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Predict: Imagine a small pond with just 4 water lilies. Guess how many lilies will be in the pond just a month later:

Answer:

Answer

2
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The value 1.106 represents:

Answer:

The daily growth factor is 1.106, meaning the water lily population grows by 10.6% each day.

3

Did the water lilies double?

Answers:
Selection 1:Yes
Selection 2:Approximately
4

0 days: 1 day: 2 days: 3 days: 4 days: 5 days:

Answer:

1

5

10 days: 15 days: 20 days: 25 days: 30 days:

Answer:

1024

6

Your prediction on the previous page was .

A
way too low
B
too low
C
about right
D
too high
E
way too high
7

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
8

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

A
a steady
B
an increasing
C
a decreasing
9

function would be most suitable to model these data.

A
A logarithmic
B
An exponential
C
A linear
D
A quadratic
10

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.
11

In terms of the water lily population change, the value 3.915 represents:

Answer:

The initial number of water lilies, approximately 4, which matches the data.

12

Which of the following did you include in your description?

A
The value of 3.915 is the initial number of water lilies.
B
It is approximately 4, which matches the data.
C
The value 1.106 is the growth rate.
D
The rate represents growth for each day.
E
The percentage growth each day is 10.6%
13

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
14

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

Answer:

7

15

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
16

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

17

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
18

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

19

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.

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Modeling with Exponential and Logarithmic Equations