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Homework Statement
A bacteria culture starts with 840 bacteria and grows at a rate proportional to its size. After 3 hours there will be 2520 bacteria.
How long will it take for the population to reach 1030 ?
2. The attempt at a solution
dP/dt = k*P
dP/P = k*dt
*Integrated both sides
ln |P| = k*t + C
P = e^(k*t + C)
*Used (0, 840) as initial values
840 = e^(k*0 + C)
C = ln840
P = e^(k*t + ln840)
P = 840e^(k*t)
*Used (3, 2520) to solve for k
P = 840e^(k*t)
2520 = 840e^(k*3)
k = 0.366
*Solved t when P = 1030
P = 840e^(0.366*t)
1020 = 840e^(0.366*t)
t = 0.557
I submit this as the answer on Webwork but it says the answer is wrong; can anyone explain to me why?