Question

In 2010, the population of a city was about 187,000. During the next 10 years, the population increased by about 1% each year. Write an exponential model that represents the population y of the city t years after 2010. Then estimate the population in 2020. Round your answer to the nearest thousand.

Answer 1

`\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &187000\\ r=rate\to 1\%\to (1)/(100)\dotfill &0.01\\ t=years \end{cases} \\\\\\ A = 187000(1 + 0.01)^(t) \implies A=y = 187000(1.01)^t \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{in 2020 is 10 years later}}{y=187000(1.01)^(10)}\implies y\approx 207000`

Answer 2

The exponential model for the population of the city t years after 2010 is given by:

y = 187,000 × 1.01^t

The population in 2020 can be estimated to be 187,000 × 1.01^10 = 200,270, which is rounded to 200,000.

Hope this helps! Have a nice day. :)