Exercises 2.2separates if we divide byPand multiply bydt.Z1PdP=r100Zdt⇒lnP=r100t+C⇒P(t)=Kert/100,whereKis the initial amount of money in the savings account,K= $1000, andr%istheinterest rate,r= 5. This results inP(t) = 1000e5t/100.(2.7)(a)To determine the amount of money in the account after 2 years we substitutet=2intoequation (2.7), which givesP(2) = 1000e10/100= $1105.17.(b)To determine when the account will reach $4000 we solve equation (2.7) fortwithP= $4000:4000 = 1000e5t/100⇒e5t/100=4⇒t=20ln4≈27.73 years.(c)To determine the amount of money in the account after 312years we need to determinethe value of each $1000 deposit after 312years has passed. This means that the initial$1000 is in the account for the entire 312years and grows to the amount which is givenbyP0= 1000e5(3.5)/100. For the growth of the $1000 deposited after 12 months, we take
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.