Question

supposed the population of a city is given by the equation

$p(t)=100,000e^{0.05t}$

where $t$ is the number of years from the present time. how large is the population now?

the population now is

question help: video ebook

Explanation:

Step1: Substitute \( t = 0 \) into the population formula

Since "now" means \( t=0 \), substitute \( t = 0 \) into \( P(t)=100000e^{0.05t} \).
We get \( P(0)=100000e^{0.05\times0} \).

Step2: Simplify the exponential term

According to the property \( a^0 = 1\) (\(a
eq0\)), for \( e^{0.05\times0}=e^{0}\), and \( e^{0}=1\).
So \( P(0)=100000\times1\).

Answer:

\(100000\)