Suppose inflation continues at rate of 5% for the next 70 years,write down a DE relating P and t, P: price of a loaf of bread t years from now.

Solve the equation to show P=Ae^0.05t ,where A is an arbitrary constant.Given that a loaf of bread costs $1 from now,how much it costs after 50 years from now?

Is the DE a good model of real world situation?

I just need help with forming the DE,i've been thinking for 3 hours,using compound interest formula then subtracting the initial price,but since there's no symbol for initial price its a bit weird.I did backward induction,but cant without knowing A.

Besides the DE, i would like to know where to sub in the $1 since initial price is not in the equation to be shown.

Also, reason why DE is not a good model of real world is it because inflation isnt constant?