Question

The population of a city is p=2500 e^(kt) where t = 0 represents the year 2000. in 1945 the population was 1350. Find the value of k and use this result to predict the population in the year 2010.

Answer 1

if the year 2000 matches t = 0, then
the year 1945 matches t = -55

so we have 1350 = 2500e^(-55k)

.54 = e^(-55k)
using natural logs,

-55k = ln(.54)
k = .011203384

so the equation is p = 2500e^(.011203384t)

in 2010 , t = 10
so
p = 2500E(.011203384*10)
= 2796

Answer 2

You are a god.