Question

The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.

CITY LIMIT

BROOKFIELD

POP. 315,000

Write an exponential growth function that represents the population t years after 2000

What will the population be in 2020? Round your answer to the nearest thousand

The population will be about

Answer 1

The exponential growth function for the population increasing by 2% annually is P(t) = 315,000 × (1.02)^t. In 2020, 20 years after 2000, the population would be about 468,000 when rounded to the nearest thousand.

Step-by-step explanation:

The exponential growth function that represents the population t years after 2000 when the population is increasing by 2% annually is given by:

P(t) = P0 × (1 + r)^t

Where:

• P0 is the initial population size, which is 315,000.
• r is the annual growth rate, which is 0.02.
• t is the number of years after 2000.

To calculate the population in 2020, we would set t to 20 years after 2000:

P(20) = 315,000 × (1 + 0.02)^20

Carrying out the calculation:

P(20) = 315,000 × 1.485947

P(20) = 467,923.52

After rounding to the nearest thousand, the population will be about 468,000 in 2020.