Question

A colony of fruit flies exhibits exponential growth. suppose that 500 fruit flies are present. let p(t) denote the number of fruit flies t days later, and let k=.08 denote growth constant.

Answer 1

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
SEE ATTACHED IMAGE.

Part A:
The differential equation is:
y '= 0.08y
The initial condition is:
P (0) = 500

Part B:
The formula for this case is:
P (t) = 500exp (0.08 * t)

Part C:
After five days we have to evaluate t = 5 in the equation.
We have then:
P (5) = 500 * exp (0.08 * 5)
P (5) = 745.9123488
Rounding:
P (5) = 746