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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A logarithmic✔ An exponentialA linearA quadratic 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:
Blank 1:
Blank 2:1.106
4

Day 10: plants

Answer:

10

5

Day 17: plants

Answer:

22

6

Did the water lilies double? Yes✔ ApproximatelyNo

A
Yes
B
✔ Approximately
C
No
7

The data show that the population of lily pads has a steady ✔ an increasing a decreasing growth rate.

A
a steady
B
✔ an increasing
C
a decreasing
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

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

Answer:

The value 3.915 represents the initial number of water lilies (the y-intercept), which is approximately 4. The value 1.106 represents the growth factor, indicating that the population grows by about 10.6% each day.

10

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%
11

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
12

Question text not available

Answers:
Selection 1:Yes
Selection 2:Approximately
13

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

Answers:
Blank 1:4
Blank 2:8
Blank 3:10
Blank 4:22
14

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:

PENDING

15

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

16

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
17

The value 1.106 represents:

Answer:

The value 3.915 is the starting amount of water lilies, and 1.106 is the daily growth factor, meaning the population increases by 10.6% daily.

18

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

Answer:

7

19

Day 7: plants

Answer:

8

20

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