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zaharov [31]
3 years ago
13

34. The amount of money in an account with continuously compounded interest is given by the formula 1

Mathematics
1 answer:
kirill115 [55]3 years ago
4 0

Answer:

Step-by-step explanation:

I have no idea what formula that is you're using but the one I teach in both algebra 2 and in precalculus for continuous compounding is

A(t)=Pe^{rt}

where A(t) is the amount after the compounding, P is the initial investment, ee is Euler's number, r is the interest rate in decimal form, and t is the time in years. If our money doubles, we just have to come up with a number which will be P and then double it to get A(t). It doesn't matter what number we pick to double, the answer will come out the same regardless. I started with 2 and then doubled it to 4 and filled in the rest of the info given with time as my unknown:

4=2e^{(.062)(t)}

Begin by dividing both sides by 2 to get

2=e^{.062t}

The only way we can get that t out of its current position is to take the natural log of both sides. Natural logs have a base of e, so

ln_e(e)=1 This is because they are inverses of one another. Taking the natural log of both sides:

ln2=.062t Now divide by .062 to get

t = 11.2 years

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