in P(t) = 500 e^kt
it depends whether you want to to be in minutes or hours.
let's do it for minutes, then
1000 = 500 e^15k
2 = e^15k
15k = ln2
k = (ln2)/15
if you want t to be hours then use .25 for t in
1000 = 500 e^.25K
K = ln2/.25 or K = 4ln2
okay, so then in 87 minutes what would it be?
let's use our first one, the one in minutes
P(87) = 500 e^(87*ln2/15)
= 500 e^4.020254
is our answer reasonable??
remember it doubles every 15 min
so after 15 min --> 1000
after 30 min ---> 2000
after 45 min ---> 4000
after 60 min ---> 8000
after 75 min ---> 16000
after 90 min ---> 32000
we could check to see if we get 32000 for 90 minutes
P(90) = 500 e^(90*ln2/15)
= 500(64) = 32000 YES!!!!
whao! that makes so much sense.
just a quick question, how do u know what e is?
thanks so much
e is one of these very strange transcendental numbers like pi
one defn of e is
1 + 1/1! + 1/2! + 1/3! + ... to infinitity
where something like 5! = 1*2*3*4*5
e = Limit (1 + 1/n)^n where n approaches infinitity
The Swiss/German mathematician Euler spent a lot of time with the concept of that number and e is often called Euler's number
e is approximately 2.71828
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