Question

The current student population of Atlanta is 2700 . If the population decreases at a rate of 6.2% each year. What will the student population be in 4 years? Write an exponential growth model for the future population P(x) where x is in years: P(x)= What will the population be in 4 years? (Round to nearest student)

Answer 1

The future population of Atlanta after 4 years will be approximately 2,090 students, calculated using an exponential decay model with the current population and annual decrease rate.

Step-by-step explanation:

The student's question concerns the future population of Atlanta given its current population size and annual rate of decrease. To find the future population, we use an exponential decay model.

Given the current population P0 of 2,700 and an annual decrease rate of 6.2%, the formula for the population P(x) after x years is P(x) = P0 × (1 - r)x, where r is the decimal form of the rate of decrease.

For a decrease rate of 6.2%, r is 0.062. So, our population model becomes P(x) = 2,700 × (1 - 0.062)x. To find the population in 4 years, substitute x with 4.

P(4) = 2,700 × (1 - 0.062)4 = 2,700 × (0.938)4 ≈ 2,700 × 0.7744 ≈ 2090.08. Therefore, after rounding, the population is expected to be 2,090 students in 4 years.