Question

The population of a city (in millions) at time t (in years) is P(t)= 2.8 e^{0.003 t}, where t=0 is the year 2000. When will the population double from its size at t=0?

Answer 1

do you know what the population is when t=0 ? (replace t with 0 in the equation, what do you get?)

Answer 2

2.8

Answer 3

and double that is 2*2.8= 5.6

that means solve for t
\[ 2.8 e^{0.003 t} = 5.6 \]
first divide both sides by 2.8 to get
\[ e^{0.003 t} = 2 \]

next, take the natural log i.e. ln of both sides