Help! differential equation problem!!?

Suppose we deposit 5000 a savings account with interest accruing at the rat of 5% compounded continuously. If we let A(t) denote the amount of money in the account at time t, then the differential equation for A is:





dA/dt = 0.05A





(a) Find the particular solution for A





(b) Assuming interest never change, how many money we will have after 10 years?





(c) We decide to withdraw $1000 (mad money) from the account each year in a continuos way beginning in year 10, how long will this money last?|||a) for t=0 A(t)=5000





we have dA/A=0.05dt


ln(A)=0.05dt+C


A=exp(0.05t+C) or A=Bexp(0.05t)


for t=0 A=5000=B


the particular solution is 5000exp(0.05t)





b)setting t=10 we have A(10)=5000exp(10*0.05)=8243.6





c)Assuming the interest keeps accruing we have


the equation 0=8243.6exp(0.05t)-1000t





You will need to solve by trial and error.





RVM