Video: Forming and Evaluating Exponential Functions Involving Exponential Growth

Rhodri Jones

The population of a city is increasing by 3.1% annually. Given that the current population is 1.7 million, and assuming that the growth rate remains constant, find the population of the city in 8 years time. Give your answer in units of millions correct to two decimal places.

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Video Transcript

The population of a city is increasing by 3.1 percent annually. Given that the current population is 1.7 million and assuming that the growth rate remains constant, find the population of the city in eight years’ time. Give your answer in units of millions, correct to two decimal places.

As the population is increasing by 3.1 percent per year, our multiplier is 1.031. We calculate this by adding 3.1 percent to 100 percent and then dividing by 100. 100 plus 3.1 is 103.1. Dividing this by 100 is 1.031.

The other two key bits of information from the question are that the initial population was 1.7 million and the number of years was equal to eight. We can therefore calculate the new population in eight years’ time by multiplying 1.7 by 1.031 to the power of eight. We multiply the initial population by the multiplier to the power of the number of years.

Typing this into our calculator gives us an answer of 2.17 million to two decimal places. Therefore, the population of a city that is increasing by 3.1 percent annually from 1.7 is 2.17 million in eight years’ time.

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