MAT 222 Week 1 Assignment
Proportions exist in many real-world applications, and in this problem
estimating the size of the bear population on the Keweenaw Peninsula. By comparing
data from two experiments, conservationists are able to predict patterns of animal
increase or decrease. In this situation, 50 bears were captured and tagged and released to
estimate the size of the bear population. A year later, after capturing a random sample of
100 bears only 2 of the bears captured were tagged bears. These proportions will be used
to determine the bear population on the peninsula. This new bear scenario can be solved
by applying the concept of proportions which allows the assumption of the ratio of
originally tagged bears to the whole population is equal to the ratio of recaptured tagged
bears to the size of the sample. To determine the estimated solution, the bears will be the
extraneous variables that will be defined for solving the proportions used.
Problem #56, page 437
The ratio of originally tagged bears to the whole population
The ratio of recaptured tagged bears to the sample size 100
50 = _2_
This is the proportion set up and ready to solve. X 100
The next step is to cross multiply.
5000 = 2X
Divide both sides by 2
2500 = X
The bear population on the Keweenaw Peninsula is estimated to be
The extreme means for this sample were 50 and 100, X and 2.
For the second problem in this assignment, the equation must be solved for Y.
Continuing the discussion of proportions, a single fraction (ratio) exists on both sides
of the equal sign so basically it is a proportion, which can be solved by cross
References: Elementary and Intermediate Algebra, 4th Ed., Dugopolski
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