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Introduction to Exponential Relationships practice problems answer
key
Imagine that you live in an old, weathered, slightly battered house. You see
a little mouse in your kitchen. Unfortunately for you, this mouse is in the
very early stages of mouse pregnancy. What you don’t consider is that this
mouse will have a litter soon, that will reproduce according to the
following:
On average, your mouse population (beginning with this one tiny, pregnant
individual) will have a litter every three months. Assume that each mouse
will only have one litter (not, of course, true) and then die, and that only six
of each litter will survive to have a litter of its own.
A. Complete the following table for the growing mouse population in your
home:
Number of generations
1
2
3
4
Time
(months)
3
6
9
12
Population size
(mice)
6
36
216
1,296
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B. Plot this population growth on the graph paper provided (as best you
can!) This is what exponential relationships look like.


How easy is it for you to predict your population size in 15 months
from this graph? Not very easy
Why? Because the curve rises so steeply
C. Now, take the log of each of your population numbers and fill in the
table below.
Number of
generations
Time
(months)
Population size
(mice)
1
2
3
4
3
6
9
12
6
36
216
1,296
Log of
population
size
0.778
1.556
2.334
3.113
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D. Plot the log of the population vs. months on the graph paper provided.
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

How does the shape of this curve compare to the shape of the curve
in B? It is linear, rather than rise steeply as a curve
How easy is it for you to predict your population size in 15 months
from this graph of log of population vs. months? Easy because it is
linear
Record your prediction: __________________
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E. Plot the population vs. months on the semi-log paper provided.



How does the shape of this curve compare to the shape of the curves
in B? In D? It is linear, and looks the same as in part D (the log of
population vs. time)
How easy is it for you to predict your population size in 15 months
from this graph on semilog paper? Easy—read off the y-axis!
Record your prediction: __________________
F. Write an equation for the population increase based on your data:
N = N0*6t
Where N is the number of mice after a given generation, “t”, and N0 is the
starting number of mice.