Expert: Sherman D. - 1/12/2004

Question
Hi, please help me with this problem. Thank you for your help! I really appreciate it!
On the day a person was born, a deposit of 50000 was made in a trust fund that pays 8.75% interest, compounded continuously.
(I don't understand what compounded continuously means.)
Find the balance on the person's 35th birthday.
Sorry to bother you but here is one more problem that won't take much calculation.
A bacteria culture starts with 500 bacteria and 5hr later has 4000 bacteria.
Find an expression for the number of the bacteria present after t hours.


Answer
Interest Compounded Continually
When interest is compounded continually (in other words, when 'n' approaches infinity), the compound interest equation takes the form:

P = A*e^rt
where e is approximately 2.71828 (the exponential number).

Found at http://colbycc.edu/www/math/general/interest.htm

so

P = 50000 * (2.71828)^(.0875 * 35)
P = 50000 * (2.71828^3.0625)
P = 50000 * 21.38089871444909992999421815693
P = $1069044.94 rounded to the nearest cent.

-----------------------------------------------------------

500/t = 4000/5
2500 = 4000t
t = 0.625 hours or 37.5 minutes
so
i guess this is right. You have 1 bacteria every 37.5 minutes.