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In a company's first year in operation, it made an annual profit of $129,000. The profit of the company increased at a constant 25% per year each year. How much total profit would the company make over the course of its first 8 years of operation, to the nearest whole number?
Answer: ◻

In a company's first year in operation, it made an annual profit of $\$129,000$ . The profit of the company increased at a constant $25\%$ per year each year. How much total profit would the company make over the course of its first $8$ years of operation, to the nearest whole number? $\newline$ Answer: ◻

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Exponential growth and decay: word problems

Full solution

Q. In a company's first year in operation, it made an annual profit of

\$129,000

. The profit of the company increased at a constant

25\%

per year each year. How much total profit would the company make over the course of its first

8

years of operation, to the nearest whole number?

\newline

Answer: ◻

Initial Profit Calculation: First year profit is $\$129,000$ . The profit increases by $25\%$ each year. $\newline$ To find the profit for each year, we multiply the previous year's profit by $1.25$ (since a $25\%$ increase is the same as multiplying by $1.25$ ).
Yearly Profit Calculation: Year $1$ profit: $\$129,000$ . Year $2$ profit: $\$129,000 \times 1.25$ .
Year $2$ Profit Calculation: Calculate Year $2$ profit: $\$129,000 \times 1.25 = \$161,250$ .
Year $3$ Profit Calculation: Year $3$ profit: $\$161,250 \times 1.25$ .
Continuation of Calculation: Calculate Year $3$ profit: $\$161,250 \times 1.25 = \$201,562.50$ .
Total Profit Calculation: Continue this process for each year up to Year $8$ .
Calculation Correction: Add up all the profits from Year $1$ to Year $8$ to get the total profit.
Calculation Correction: Add up all the profits from Year $1$ to Year $8$ to get the total profit.Total profit = Year $1$ + Year $2$ + Year $3$ + ... + Year $8$ .
Calculation Correction: Add up all the profits from Year $1$ to Year $8$ to get the total profit.Total profit = Year $1$ + Year $2$ + Year $3$ + ... + Year $8$ .Oops, we need to calculate the profit for each year first before adding them up. Let's do that now.

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