Question

Please help me with this problem so I can better explain this to my son.2.Rhonda started a business. Her business made $30,000 in profits the first year. Her annual profits have increased by an average of 5% each year since then. (a)Write an iterative rule to model the sequence formed by the profits of Rhonda’s business each year.(b)Use the rule to determine what the annual profits of Rhonda’s business can be predicted to be 15 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.

Answer 1

`\begin{gathered} a)P=30000(1+0.05)^n \\ b)\$62,367.00 \end{gathered}`

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`

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}`

Note that we have plugged into n, n=15 years. Since the first year was $30,000 the profits.