Question

The population of Philadelphia was 12,000 in 2006 and is growing by 5% each year. Predict the population for 2020. Thanks!

Answer 1

we are given

Let's assume initial population in 2006

initial population 12000

$P=12000$

$r=0.05$

$t=2020-2006$

$t=14$

now, we can use formula

$A=Pe^{rt}$

we can plug values

$A=12000e^{0.05*14}$

we can solve it

and we get

$A=24165$.............Answer

Answer 2

Population at any time t is given as:

$P(t)=P(0)(1+r)^t$

So, P(t)=12000(1+0.05)^t

From, 2006 to 2020, there are 14 years, so t=14

P(14)=12000(1+0.05)^14

=12000(1.05)^14=12000*1.979

=23748

So, Population in 2020,(14 years later)=23748