Question

In 2012, the population of a city was about 207,000. During the next 8 years, the population increased by about 1% each year. Write an exponential model that represents the population y of the city t years after 2012. Then estimate the population in 2020. Round your answer to the nearest thousand. Exponential model: y= 2020 population estimate:

Answer 1

• y = 207000·1.01^t
• 224,000

Explanation:

You want an exponential model and an estimate of the population in 2020 if a city's population in 2012 was 207,000 and it increased by 1% per year.

Model

The exponential model will be of the form ...

population = (initial population) · (growth factor)^t

where the growth factor is ...

growth factor = 1 + growth rate

Using the given initial population (207000) and growth rate (1%), the population can be modeled by ...

y = 207000·1.01^t

Estimate

In 2020, t = 2020 -2012 = 8, so the population estimate is ...

y = 207000·1.01^8 ≈ 224,000

The population estimate for 2020 is 224,000.

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