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# Mathematics - Algebra

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I have attached the problems.

Ten years ago your friend invested in a plot of land with the idea of eventually building a summer cottage on it. His plan was to place a "nest egg" of \$12,000 in a long term Certificate of Deposit which paid 8% interest over a period of 20 years, compounded monthly. At the end of the 20 years, he would use the money to build the cottage.
The problem was the plot had 8 prairie dogs on it 10 years ago when he acquired the ground.
This year he made a count of the prairie dogs and found there were 102 on the same plot! A biologist friend assured him that the prairie dogs were growing exponentially according to the law of natural growth, and something needed to be done.

#1.Write the formula for natural exponential growth for this particular prairie dog population.
Hint: Find the "k" value for this population, and put it in your formula.

#2.Once you have this formula, predict:
a. approximately how many years from now will the population reach 365 prairie dogs.
b. approximately how large the population will be 10 years from now.

#3. Write the formula for compound interest and calculate how much money your friend will have on deposit (in the account described above) after 20 years (10 years from now).

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