This question has two parts Alice invests 2000 at Bobs bank

This question has two parts. Alice invests $2000 at Bob\'s bank and $7000 at Charlie\'s bank. Bob compounds interest continuously at a nominal rate of 6%. Charlie compounds interest continuously at a nominal rate of 2%. Part 1: In how many years will the two investments be worth the same amount? Your answer must be EXACT. Answers which included decimal points ANYWHERE will be marked incorrect (so convert those interest rates to fractions!). Enter an EXACT, symbolic answer (such as 3/2, not 1.5, or ln(2), not 0.69 years Part 2: When both investments are worth the same amount, how much will each be worth? IMPORTANT: Round your answer to the nearest cent. Do not include a dollar sign in your answer.

The air pressure p(h) (in lb/in²) at an altitude of h feet above sea level may be approximated by the formula

p(h) = 14.7e^0.0000385h.

(a) At approximately what altitude h is the air pressure 9 lb/in²? (Round your answer to the nearest whole number.)
h = ft

(b) At approximately what altitude h is the air pressure one-half its value at sea level? (Round your answer to the nearest whole number.)
h = ft

Solution

1) after t years worth of investment in bob\'s bank =2000e^0.06t,worth of investment in charlie\'s bank =7000e^0.02t

two investments be worth the same amount

=>2000e^0.06t =7000e^0.02t

=>e^0.06t/e^0.02t =7000/2000

=>e^0.06t-0.02t=(7/2)

=>e^0.04t=(7/2)

=>0.04t=ln(7/2)

=>t=(1/0.04)ln(7/2)

=>t=(100/4)ln(7/2)

=>t=25ln(7/2)

b) When both investments are worth the same amount,worth of each investment =2000e^{0.06*25ln(7/2)}

When both investments are worth the same amount,worth of each investment =13095.78 dollars