Posted by Vanessa on Monday, July 14, 2008 at 10:46am.
A population of 500 E. coli bacteria doubles every 15 minutes. Use this information to find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model.
so we're supposed to use P(t)= (Po)(e)^kt
so P(o) would be 500,
and then would t be 15 or 0.25 and wowhat would k be? 2?

Calculus  Reiny, Monday, July 14, 2008 at 11:43am
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

Calculus  Vanessa, Monday, July 14, 2008 at 12:51pm
okay, so then in 87 minutes what would it be?

Calculus  Reiny, Monday, July 14, 2008 at 1:42pm
let's use our first one, the one in minutes
P(87) = 500 e^(87*ln2/15)
= 500 e^4.020254
= 27857.6
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!!!!

Calculus  Reiny, Monday, July 14, 2008 at 7:18pm
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
or
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

Calculus  Anonymous, Saturday, June 16, 2012 at 6:14am
e is approximately 2.71828
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