A town has a population of 27,000 and shrinks at a rate of 8% every year. Which equation represents the town's population after 7 years? P=27,000(0.2)^(7) P=27,000(0.92)^(7) P=27,000(1-0.08)(1-0.08)(1-0.08) P=27,000(0.08)^(7)

Question

A town has a population of 27,000 and shrinks at a rate of  8% every year. Which equation represents the town's population after 7 years?  P=27,000(0.2)^(7)  P=27,000(0.92)^(7)  P=27,000(1-0.08)(1-0.08)(1-0.08)  P=27,000(0.08)^(7)

Bytelearn · Accepted Answer

Identify Initial Population and Rate: We need to find the equation that represents the population after 7 years, given an initial population and a yearly decrease rate. The initial population is 27,000, and the shrinkage rate is 8% per year, which means the population retains 100% - 8% = 92% of its size each year. To represent this mathematically, we use the formula for exponential decay: P = P0 * (1 - r)^t, where P0 is the initial population, r is the shrinkage rate as a decimal, and t is the time in years.Convert Rate to Decimal: Convert the shrinkage rate from a percentage to a decimal by dividing by 100. So, 8% becomes 0.08. This means that each year, the population is 92% of the previous year's population, which is represented as 0.92 in decimal form.Apply Exponential Decay Formula: Now, we apply the exponential decay formula with the values we have: P0 = 27,000, r = 0.08, and t = 7. The equation becomes P = 27,000 * (1 - 0.08)^7, which simplifies to P = 27,000 * (0.92)^7.Check Correct Equation: We can now check the given options to see which one matches our equation. The correct equation that represents the town's population after 7 years is P = 27,000 * (0.92)^7.

A town has a population of $27$ , $000$ and shrinks at a rate of $8 \%$ every year. Which equation represents the town's population after $7$ years? $\newline$ $P=27,000(0.2)^{7}$ $\newline$ $P=27,000(0.92)^{7}$ $\newline$ $P=27,000(1-0.08)(1-0.08)(1-0.08)$ $\newline$ $P=27,000(0.08)^{7}$

Full solution

More problems from Interpreting Linear Expressions

Related topics