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#### karush

##### Well-known member

- Jan 31, 2012

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$\tiny{\textbf{6.8.7}}$ Kiaser HS

Population Growth The population of a southern city follows the exponential law

(a) If N is the population of the city and t is the time in years, express N as a function of t.$N(t)=N_0e^{kt}$

(b) If the population doubled in size over an 18-month period and the current population is 10,000, what will

the population be 2 years from now?

$\begin{array}{rl}

2&=e^{k(1.5)} \\

\ln 2&=k \cdot 1.5\\

\dfrac{\ln 2}{1.5}&=k\\

\therefore k&\approx0.462098\\

f(t)&\approx10000e^{0.462098\cdot 2}\\

&\approx 25198

\end{array}$

well anyway hopefully ok

typos maybe