![\begin{gathered} a)P=30000(1+0.05)^n \\ b)\$62,367.00 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%29P%3D30000%281%2B0.05%29%5En%20%5C%5C%20b%29%5C%2462%2C367.00%20%5Cend%7Bgathered%7D)
1) Iteration means a repetition of a rule.
a)
Considering that we have the following data:
Rate of increase: 5% per year
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2) Then we can write out the following:
![P=30000(1+0.05)^n](https://tex.z-dn.net/?f=P%3D30000%281%2B0.05%29%5En)
Plugging into n, the number of years we'll have:
Profits: $30,000 1st year
P: $31.500 2nd year
$33075 3rd year
(...) (...)
b) Since we want to know the predicted profit 15 years from the first year, then we can plug for that:
![\begin{gathered} P=30000(1+0.05)^{15} \\ P=\$62,367.00 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%3D30000%281%2B0.05%29%5E%7B15%7D%20%5C%5C%20P%3D%5C%2462%2C367.00%20%5Cend%7Bgathered%7D)
Note that we have plugged into n, n=15 years. Since the first year was $30,000 the profits.