The population of a bacteria culture increases at the rate of 3 times the square root of the present population.

Question

A. Model the population P = P(t) of the bacteria population with a differential equation.
B. Solve the differential equation that models the population P = P(t) of the bacteria population.
C. Suppose the population at time t = 0 hours is 1000. Derive an equation for the population P as an explicit function of time t (in hours). Your equation should contain no undetermined constants.
D. What’s the population of the bacteria culture at the end of 10 hours? After 100 hours?

Answer 1

dp/dt = 3√p

dp/√p = 3dt
2√p = 3t+c
4p = (3t+c)^2

Now finish it off

Answer 2

Im confused on the function of time.
Would it be
p = (3x+20√10)^2 / 4
p = (3x^2 / 4) + 1000

Answer 3

p(0) = 1000, so
4000 = c^2
c = 20√10
p = (3x+20√10)^2 / 4

Odd that you should even consider the 2nd equation, by this time in your math studies.