SOLUTION: 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 Cert
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Question 91829: 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.
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).
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
en 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.
:
8*(e^10k) = 102
e^10k = 102/8
10k*ln(e) = ln(102/8)
10k = ln(2.54553); ln of e is 1
k = 2.54553/10
k = .255
:
The formula A = Ao(e^.255t); Ao=original amt, t=time in years
2. Once you have this formula, predict:
a. approximately how many years from now will the population reach 365 prairie dogs.
102*(e^.255t) = 365
ln(e^.255t) = ln(365/102)
.367t*ln(2) = ln(365/102)
.367t*.693147 = 1.275
.254385t = 1.275
t = 5 years
:
b. approximately how large the population will be 10 years from now.
A = 102*(2^.367(10))
A = 102*(2^3.67); use a good calc here:
A = 1300 critters 10 yrs 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).
:
Compound Int formula: A = P *
In 20 yrs:
A = 12000 *
A = 59,121.63
:
In 10 yrs:
A = 12000 *
A = 26,635.68
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