1 There were 27 deer in a park on January 1 2000 Six months

1. There were 27 deer in a park on January 1, 2000. Six months later there were 38 deer in the same park. Assume the number of deer in the park with respect to the number of months since January 1, 2000 can be modeled by an exponential function.

a. Determine the 6-month growth factor.

b. Determine the 6-month percent change.

c. Determine the 1-month growth factor.

d. Determine the 1-month percent change.

e. Define a funtion, g, that relates the number of deer in the park in terms of the number of months that have elapsed since January 1, 2000, n. (Assume the number of deer continues to increase by the same percent each month).

2. Suppose the population of a town increased or decreased by the following percentages. For each situation, find the annual percent change of the population.

a. Decreases by 28% every 14 years.

Solution

There were 27 deer in a park on January 1, 2000. Six months later there were 38 deer in the same park.

1) 6 month growth factor =38_/27=1.4074

2)6-month percent change=(1.4074-1)*100%

6-month percent change=40.74%

3)1 month growth factor =(38_/27)^1/6=1.0586

4)1-month percent change=(1.0586-1)*100%

1-month percent change=5.86%

e) funtion, g, that relates the number of deer in the park in terms of the number of months that have elapsed since January 1, 2000, n. is g(n) =27*1.0586ⁿ

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