Question

The population of a city was 195 thousand in 1992. The exponential growth rate was 1.2% per year.

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a) Find the exponential growth function in terms of t, where t is the number of years since 1992.


P(t)=____

Answer 1

well, we know that it was 195 in 1992, so "t" years later that'd be

`\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &195\\ r=rate\to 1.2\%\to (1.2)/(100)\dotfill &0.012\\ t=years\dotfill &t\\ \end{cases} \\\\\\ A=195(1 + 0.012)^(t) \implies A =195(1.012)^t`