The rate of growth dP/dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 9, where P is the population size and t is the time in days (0 ≤ t ≤ 10). The initial size of the population is 700. Approximate the population after 7 days. Round the answer to the nearest integer.
dP/dt = k√t
not sure where this "constant coefficient" comes in. If you meant √(9t), then that is just 3√t, which just becomes part of k. I'll ignore it, and you can adjust things as needed.
P = 2/3 k t^(3/2) + c
P(0) = c = 700
Have at it.