MHB How does the population of a southern city follow the exponential law?

[karush]

$\tiny{\textbf{6.8.7}}$ 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 :unsure:
typos maybe

 

[topsquark]

I didn't check the numbers but the logic is correct.

-Dan

 

[HOI]

Since you stated your basic equation as
$N(t)= N_oe^{kt}$
I would have preferred that you write
$2N_0= N_0e^{1.5k}$
before you divide both sides by $N_0$ to get
$2= e^{1.5k}$.

But I realize that is being petty!