Question

a citys population is increasing at a rate of 5% per year if the growth rate remains the same and the population is 550000 in the year 2020 approximately how many people will be here in 15 years

Answer 1

Using the exponential growth formula, the city's population, currently at 550,000 and growing at 5% per year, will approximately reach 1,175,000 in 15 years.

Step-by-step explanation:

The student's question involves calculating future population size based on a constant growth rate, which is a mathematical problem that can be solved using the concept of exponential growth. Given a current population of 550,000 and an annual growth rate of 5%, we can use the formula for exponential growth:

P(t) = P0 × (1 + r)t

Where:

• P(t) is the population at time t
• P0 is the initial population size (550000)
• r is the growth rate (0.05 for 5%)
• t is the number of years into the future (15 years)

Applying these numbers to the formula:

P(15) = 550000 × (1 + 0.05)15

Calculating the expression gives us:

P(15) ≈ 550000 × (1.05)15 ≈ 1175000 (Approximately)

Therefore, if the population growth rate of 5% per year remains the same, the population of the city will be approximately 1,175,000 in 15 years, which is the year 2035.