Joe invested $5, 200 in an account earning 3.8% annual interest that is compound

Question

Joe invested $5, 200 in an account earning 3.8% annual interest that is compounded monthly. How long will it take to accumulate a total of $6, 200 in the account? Mary has $3, 500 in a savings account earning 4 1/2% annual interest that is compounded continuously. How long will it take to double the amount in the account? During the exponential growth phase, certain bacteria can grow at a rate of 5.3% per hour. If 12,000 cells are initially present in a sample, construct an exponential growth model and use It to: a. Estimate the population of bacteria in 3.5 hours, b. Estimate the time it will take the population to double.

Explanation / Answer

22) Compounded monthly : A = P(1 +r/12)^(12n)

P = $5200 ; r/12=0.038/12 = , A = $ 6200 ; n = ?

6200 = 5200(1 + 0.003167)^12n

1.192 = 1.003167^12n

ln(1.191)/ln(1.003167) = 12n

n = 55.27/12 = 4.6 yrs

24) N = No(1+r)^t

No = 12000 ; r = 0.053

In t = 3.5hrs ; N = 12000(1.053)^3.5 = 14377.406 bacterias

Double the popultaion : 24000 = 12000(1.053)^t

t = ln(2)/ln1.053 = 13.42 hrs

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