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August 21, 2014

August 21, 2014

Posted by **Vanessa** on Monday, July 14, 2008 at 10:46am.

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 11:43amin 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 12:51pmokay, so then in 87 minutes what would it be?

- Calculus -
**Reiny**, Monday, July 14, 2008 at 1:42pmlet'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 -
**Vanessa**, Monday, July 14, 2008 at 1:59pmwhao! that makes so much sense.

just a quick question, how do u know what e is?

thanks so much

<3333333333

- Calculus -
- Calculus -
**Reiny**, Monday, July 14, 2008 at 7:18pme 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 6:14ame is approximately 2.71828

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