The population of a city is modeled by the equation P(t)=262,576e^0.25t where t is measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?
Round your answer to the nearest hundredth of a year (i.e. 2 decimal places).
The population will reach one million in______ years.
- stanschimLv 71 month agoFavorite Answer
1,000,000 = 262,576e^0.25t
Taking natural logarithms of both sides gives:
ln(1,000,000) = ln(262,576e^0.25t)
ln(1,000,000) = ln(262,576) + ln(e^0.25t)
ln(1,000,000) = ln(262,576) + 0.25t
t = [ln(1,000,000) - ln(262,576)] / 0.25
t =5.35 years
- az_lenderLv 71 month ago
1000000/262576 = e^(0.25 t) =>
ln(1000000/262576) = 0.25 t =>
ln(3.8084) = 0.25 t =>
t = 5.35 years.