# 6.8.7 Population Growth

#### karush

##### Well-known member
$\tiny{\textbf{6.8.7}}$ 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

#### topsquark

##### Well-known member
MHB Math Helper
I didn't check the numbers but the logic is correct.

-Dan