Ok, here's the problem:

Investment. LetA(t)be the amount in a fund earning interest at the annual rate ofr, compounded continuously. If a continuous cash flow ofPdollars per year is withdrawn from the fund, then the rate of decrease ofAis given by the differential equation

where when

(a) Solve this equation forAas a function oft.(b) Use the result of part (a) to find

Awhen =$2,000,000, r=7%, P=$250,000, and t=5 years

(c) Find if a retired person wants a continuous cash flow of $40,000 per year for 20 years. Assume that the person's investment will earn 8%, compounded continuously.

Ok, so C is simple enough once A and B is done since you basically just plug in for the variables. Part A & B is what's getting me. Here's what I did.

I rearranged it into a first-order linear DE so and my so the IF is

Then I multiplied the original equation on both sides by the IF to get

From there...

What's tripping me up isonlywhen so I'm not sure how to proceed.

I can set and plug in for with the above general soln to get

but then part B asks me to input t as one of the variables and doesn't show up in this new soln so I'm not sure where to go from here.