A town has a population of 118,600 and grows at a rate of 5% every year. Which equation represents the town's population after 4 years? P=118,600(1+0.05)^(4) P=118,600(1+0.05) P=118,600(0.05)^(4) P=118,600(0.95)^(4)

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A town has a population of 118,600 and grows at a rate of  5% every year. Which equation represents the town's population after 4 years?  P=118,600(1+0.05)^(4)  P=118,600(1+0.05)  P=118,600(0.05)^(4)  P=118,600(0.95)^(4)

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Identify initial population and growth rate: Identify the initial population and the growth rate. The initial population of the town is 118,600, and the growth rate is 5% per year, which can be written as 0.05 in decimal form.Determine exponential growth formula: Determine the formula for exponential growth. The general formula for exponential growth is P = P0(1 + r)^t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the time in years.Plug in values for formula: Plug in the values for the initial population, growth rate, and time into the formula. Using the formula from Step 2, we substitute P0 = 118,600, r = 0.05, and t = 4 to get the equation P = 118,600(1 + 0.05)^4.Check other options: Check the other options to ensure they do not represent the correct formula. Option B: P = 118,600(1 + 0.05) does not account for the compounding effect over 4 years. Option C: P = 118,600(0.05)^4 only considers the growth rate raised to the power of 4, which is incorrect. Option D: P = 118,600(0.95)^4 suggests a decrease by 5% each year, which is not the case.

A town has a population of $118$ , $600$ and grows at a rate of $5 \%$ every year. Which equation represents the town's population after $4$ years? $\newline$ $P=118,600(1+0.05)^{4}$ $\newline$ $P=118,600(1+0.05)$ $\newline$ $P=118,600(0.05)^{4}$ $\newline$ $P=118,600(0.95)^{4}$

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