Question

On January 2015 the population of Franktown was 35,000 people end it has been increasing at a steady rate of 1.7% annually. Estimate the population of Franktown on January 1, 2019 during. what years did the population of Franktown first exceed 50,000 people?

Answer 1

Using the exponential growth formula, the population of Franktown on January 1, 2019, is estimated to be approximately 37,453 people. To find when the population first exceeds 50,000, solve the equation involving the initial population, growth rate, and time using logarithms.

Step-by-step explanation:

To estimate the population of Franktown on January 1, 2019, we can use the formula for exponential growth, which is:

P = P0(1 + r)t

where:

• P is the future population,
• P0 is the initial population,
• r is the annual growth rate,
• t is the number of years.

Plugging in the values for Franktown, with P0 = 35,000, r = 0.017 (1.7%), and t = 4 years (from 2015 to 2019), we get:

P = 35,000(1 + 0.017)4

Performing the calculation:

P ≈ 35,000(1.017)4

P ≈ 35,000(1.0701)

P ≈ 37,453

Thus, the estimated population of Franktown on January 1, 2019, is approximately 37,453 people.

To determine when Franktown first exceeded a population of 50,000 people, we would need to set up the equation and solve for t when P = 50,000. This would require logarithms to solve for t. The exact year would be found by solving the equation 50,000 = 35,000(1.017)t for t.