supposed the population of a city is given by the equation\n\n$p(t)=100,000e^{0.05t}$\n\nwhere $t$ is the…

supposed the population of a city is given by the equation\n\n$p(t)=100,000e^{0.05t}$\n\nwhere $t$ is the number of years from the present time. how large is the population now?\n\nthe population now is\n\nquestion help: video ebook

supposed the population of a city is given by the equation\n\n$p(t)=100,000e^{0.05t}$\n\nwhere $t$ is the number of years from the present time. how large is the population now?\n\nthe population now is\n\nquestion help: video ebook

Answer

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\neq0)), for ( e^{0.05\times0}=e^{0}), and ( e^{0}=1). So ( P(0)=100000\times1).

Answer:

(100000)