SOLUTION: A mathematical model for world population growth over short periods of time is given by P = P(0)e^rt where P(0)= population at t=0, r = rate compounded continuously, t = time in ye

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A mathematical model for world population growth over short periods of time is given by P = P(0)e^rt where P(0)= population at t=0, r = rate compounded continuously, t = time in ye      Log On


   

Question 944492: A mathematical model for world population growth over short periods of time is given by P = P(0)e^rt where P(0)= population at t=0, r = rate compounded continuously, t = time in years, and P = population at time t.
How long will it take the earth's population to double if it continues to grow at its current rate of 2% per year(compounded continuously)?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
P=P%5Bo%5De%5E%28rt%29

2=1%2Ae%5E%28rt%29

e%5E%28rt%29=2

ln%28e%5E%28rt%29%29=ln%282%29

rt%2A1=ln%282%29

t=%281%2Fr%29%28ln%282%29%29

2% means 0.02.

t=%281%2F0.02%29ln%282%29

highlight%28t=35%29 years.