SOLUTION: please help me solve this problem population p grows according to the equation dp/dt=kp where k is a constant and t is measured in years. if the population doubles every 12 years

Question 192043: please help me solve this problem
population p grows according to the equation dp/dt=kp where k is a constant and t is measured in years. if the population doubles every 12 years then the value of k is approximately
a) 3.585
b)1.792
c)0.693
d)0.729
e)0.058

Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
take dp/dt=kp and solve for p to get p = Ae^(kt) (it's a solution to given DE)

2A = Ae^(k*12)

2 = e^(12k)

ln(2) = 12k

Ans: k = ln(2)/12

k ~ 0.05776

Answer is e)

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