The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.4. The initial population is 10.

What is the population after 30 days?
How long does it take for the population to double?

1 answer

If you mean k=0.4 in
dP/dt = kP
then
dp/P = 0.4
lnP = 0.4t + c
P = ce^(0.4t)
P(0) = 10 means
P(t) = 10e^(0.4t)

so find P(30)
and solve for t in 10e^(0.4t) = 20