A town has a population of 120,900 and shrinks at a rate of 4.7% every year. Which equation represents the town's population after 8 years? P=120,900(1-0.047) P=120,900(1+0.047)^(8) P=120,900(1-0.47)^(8) P=120,900(0.953)^(8)

Question

A town has a population of 120,900 and shrinks at a rate of  4.7% every year. Which equation represents the town's population after 8 years?  P=120,900(1-0.047)  P=120,900(1+0.047)^(8)  P=120,900(1-0.47)^(8)  P=120,900(0.953)^(8)

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Identify initial population and rate: Identify the initial population and the annual shrinkage rate. The initial population is given as 120,900, and the annual shrinkage rate is 4.7%.Convert shrinkage rate to decimal: Convert the annual shrinkage rate from a percentage to a decimal. To convert a percentage to a decimal, divide by 100. 4.7% as a decimal is 0.047.Determine population decrease factor: Determine the population decrease factor for one year. Since the population decreases by 4.7% each year, the factor by which the population decreases annually is 1 - 0.047.Write equation for population after 8 years: Write the equation that represents the population after 8 years. The population after 8 years can be found by multiplying the initial population by the decrease factor raised to the power of the number of years. P = initial population * (decrease factor)^(number of years) P = 120,900 * (1 - 0.047)^(8)Simplify decrease factor: Simplify the decrease factor. 1 - 0.047 = 0.953Substitute factor into equation: Substitute the simplified decrease factor into the equation. P = 120,900 * (0.953)^(8)Verify equation against options: Verify that the equation matches one of the given options. The correct equation is P = 120,900 * (0.953)^(8), which matches the last option.

A town has a population of $120$ , $900$ and shrinks at a rate of $4.7 \%$ every year. Which equation represents the town's population after $8$ years? $\newline$ $P=120,900(1-0.047)$ $\newline$ $P=120,900(1+0.047)^{8}$ $\newline$ $P=120,900(1-0.47)^{8}$ $\newline$ $P=120,900(0.953)^{8}$

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