A town has a population of 5.56 ×10^(4) and grows at a rate of 4% every year. Which equation represents the town's population after 7 years? P=(5.56 ×10^(4))(1+0.04)^(7) P=(5.56 ×10^(4))(1+0.04)(1+0.04)(1+0.04)(1+0.04) P=(5.56 ×10^(4))(0.04)^(7) P=(5.56 ×10^(4))(1-0.04)^(7)

Question

A town has a population of  5.56 ×10^(4) and grows at a rate of  4% every year. Which equation represents the town's population after 7 years?  P=(5.56 ×10^(4))(1+0.04)^(7)  P=(5.56 ×10^(4))(1+0.04)(1+0.04)(1+0.04)(1+0.04)  P=(5.56 ×10^(4))(0.04)^(7)  P=(5.56 ×10^(4))(1-0.04)^(7)

Bytelearn · Accepted Answer

Exponential Growth Formula: To find the population after 7 years with a growth rate of 4% per year, we use the formula for exponential growth: P = P0(1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the time in years.Given Values: The initial population P0 is given as 5.56 × 10^4. The growth rate r is 4%, which is 0.04 in decimal form. The time t is 7 years.Substitute Values: Substitute the given values into the exponential growth formula: P = (5.56 × 10^4)(1 + 0.04)^7.Correct Representation: The equation P = (5.56 × 10^4)(1 + 0.04)^7 correctly represents the population after 7 years, considering a 4% annual growth rate compounded once per year.Evaluation of Options: The other options can be evaluated for correctness: - P = (5.56 × 10^4)(1 + 0.04)(1 + 0.04)(1 + 0.04)(1 + 0.04) does not correctly apply the compound interest formula, as it only multiplies the growth factor 4 times instead of 7. - P = (5.56 × 10^4)(0.04)^7 incorrectly raises the growth rate to the power of 7 instead of applying it as a percentage increase. - P = (5.56 × 10^4)(1 - 0.04)^7 incorrectly assumes a decrease by 4% per year instead of an increase.

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