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