Video: Evaluating Exponential Growth Functions

A mathematical model predicts that the population of a country, 𝑦 million, will be given by the formula 𝑦 = 17.1(1.02)^𝑥, where 𝑥 is the number of years since 2015. Use this model to predict the population of the country, to the nearest million, in both 2021 and 2022.

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Video Transcript

A mathematical model predicts that the population of a country, 𝑦-million, will be given by the formula 𝑦 is equal to 17.1 multiplied by 1.02 to the power of 𝑥, where 𝑥 is the number of years since 2015. Use this model to predict the population of the country to the nearest million in both 2021 and 2022.

The population of the country for anytime after 2015 can be calculated by multiplying 17.1 by 1.02 to the power of 𝑥. We are asked to calculate the population in both 2021 and 2022. 2021 minus 2015 is equal to six. 2022 minus 2015 is equal to seven. These are the values of 𝑥 that we need to substitute into the equation. When 𝑥 is equal to six, 𝑦 is equal to 17.1 multiplied by 1.02 to the power of six. This is equal to 19.2573 and so on.

𝑦 is the population in millions. And we need to work out our answer to the nearest million. This means that we need to round to the nearest whole number. As the number in the tenths column, two, is less than five, we will round down. The population to the nearest million in 2021 is 19 million. We now repeat this process for 𝑥 equal to seven. 𝑦 is equal to 17.1 multiplied by 1.02 to the power of seven. This is equal to 19.6425 and so on. Once again, we need to round to the nearest whole number. As six is greater than five, this time we round up. The population in 2022 to the nearest million is 20 million.

We have therefore predicted that the population will be 19 million in 2021 and 20 million in 2022.

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