
Continuous compounding
I'm having a lot of trouble with my calculus homework. Does anyone know how to work this problem?
Suppose the consumption of electricity grows at 7.6% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.
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Possible Answers:
14.46 , 39.47 , 0.14 , 1.45

ANYBODY??? I figured the answer but am having problems with the formula. I came up with fv=p(1+r/n)^t, and cannot figure out t....my formula looks like this:
3=1(1.076)^t
help...........

I got 14.55 years  I will post how I did it in a minute  I have to get the equations into this box
Your formula should be ...
a(t) = lim as n approaches infinity ( a0(1+ r/n)^(nt) )
where a0 is the initial amount of power used, r is the rate of growth (.076) and n is the number of times it is compounded
Then you use L'Hopital's rule to find that the above function is the same as this
a(t) = a0e^(rt)
(Hopefully this helps a little)
a(t) = 3 = 1*e^(.076*t)
ln(3) = .076*t
t=ln(3)/.076 = 14.55 years

Anytime something is compounded continuously, use the formula. Or, if it is money that is being compounded continuously, use formula. Either way, the formulas are equivalent.
Or like billa said, you can use the regular compound formula and just find the .