Business Suppose you start a lawn-mowing business and make a...

Business Suppose you start a lawn-mowing business and make a profit of 400 dollars in the first year. Each year, your profit increases $5 \% .$ i. a. Write a function that models your annual profit. b. If you continue your business for $10 \mathrm{yr},$ what will your total profit be?

Business Suppose you start a lawn-mowing business and make a profit of 400 dollars in the first year. Each year, your profit increases $5 \% .$ i.
a. Write a function that models your annual profit.
b. If you continue your business for $10 \mathrm{yr},$ what will your total profit be?

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Key Concepts

Exponential Growth

Exponential growth describes a process where a quantity increases by a fixed percentage over equal time intervals. In the context of profit, this means that each year’s profit is multiplied by a constant factor, such as 1.05 for a 5% increase, leading to an exponential increase over time.

Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant, known as the common ratio. This concept is used to model annual profit when the profit increases by a fixed percentage each year.

Summation of a Geometric Series

The summation of a geometric series involves adding together the terms of a geometric sequence. This is useful for calculating the total profit over a period of several years when the profit increases exponentially, as it provides a formula to find the sum of all the individual yearly profits.

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