Math  /  Algebra

QuestionTwo towns experience changes in population. Equations modelling the population of each town, where PP is population and tt is the number of years after January 1, 2021, are shown below.  Town A PA=7000(0.93)t Town B PB=2500(1.12)t\begin{array}{c} \text { Town A } \rightarrow P_{A}=7000(0.93)^{t} \\ \text { Town B } \rightarrow P_{B}=2500(1.12)^{t} \end{array}
The number of years, to the nearest tenth, that it will take for the population of the two towns to be the same. t= years t=\square \text { years }

Studdy Solution
Calculate the value of t t using a calculator and round to the nearest tenth:
tln(2.8)ln(1.12)ln(0.93)14.3 t \approx \frac{\ln(2.8)}{\ln(1.12) - \ln(0.93)} \approx 14.3
The number of years it will take for the populations to be the same is:
14.3 years \boxed{14.3} \text{ years}

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