a town has a population of 2.33 × 10⁴ and grows at a rate of 7% every year. which equation represents the…

planation:

Step1: Recall the exponential growth formula

The formula for exponential growth is ( P(t) = P_0(1 + r)^t ), where ( P_0 ) is the initial population, ( r ) is the annual growth rate (in decimal form), and ( t ) is the time in years.

Step2: Identify the given values

Here, the initial population ( P_0 = 2.33\times 10^{4} ), the growth rate ( r = 7% = 0.07 ), and the time ( t = 6 ) years.

Step3: Substitute the values into the formula

Substituting these values into the exponential growth formula, we get ( P(6)=2.33\times 10^{4}(1 + 0.07)^{6} ), which simplifies to ( P(6)=2.33\times 10^{4}(1.07)^{6} ).

Answer:

The equation representing the town's population after 6 years is ( P(6)=2.33\times 10^{4}(1.07)^{6} ) (where ( P(6) ) is the population after 6 years).