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Mathematics

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In 1960, the population of a town was 14 thousand people. Over the course of the next 50 years, the town grew at a rate of 30 pe

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SOLUTIONS

Given: Assume y is the population

$\begin{gathered} t=0=1960,y=14030 \\ t=1=1961,y=14060 \\ so\text{ b = 14000} \\ so\text{ k = 30} \end{gathered}$

The town grow at the rate of 30 people per year.

$y=kt+14000$ $y=30t+14000$

(A) The population predicted to be in 2030 will be

$\begin{gathered} 2030-1960=70 \\ y=30k+14000 \\ y=30(70)+14000 \\ y=2100+14000 \\ y=16100people \end{gathered}$

(B) so when y = 15000, find t

$\begin{gathered} y=15000 \\ y=30t+14000 \\ 15000=30t+14000 \\ 15000-14000=30t \\ 1000=30t \\ t=\frac{1000}{30} \\ t\approx33 \\ t=1960+33 \\ t=1993 \end{gathered}$

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