Thread: Exponential Growth and Logarithms

So, I have these two problems for Calculus that I'm rather stuck on right now.

The information given for the first is this:

(Exponential growth)
Colony weight:
15 mg at 9:00 A.M.
25 mg at 11:30 A.M.
45 mg at ?

where 9:00 A.M. corresponds to t=0.

What's given for the next one is this:

"In the cold storage room, which is maintained at a constant temperature of 20° C, Detective Marino discovered the body of Dr. Expo’s assistant, Nat Log. The Detective measured the temperature of the body to be 34° C at 5:00 p.m. Two hours later, when Dr. Kay Scarpetta, the chief medical examiner, arrived to examine the bodies and evidence, she measured Nat’s body temperature to be 31.7° C.
Dr. Scarpetta knew that Newton’s Law of Cooling says that the temperature of a cooling object is given by the function

T

(t)=Se−kt+M

where M is the temperature of the surrounding environment, although she didn’t know either S or k. She did know that the normal body temperature of a living person is 37° C. "

And I'm supposed to find the missing times for both. Any help would be greatly appreciated!

Originally Posted by Rumor

The information given for the first is this:

(Exponential growth)
Colony weight:
15 mg at 9:00 A.M.
25 mg at 11:30 A.M.
45 mg at ?

where 9:00 A.M. corresponds to t=0.

you should already be acquainted with the general equation for uninhibited exponential growth ...



for your first problem ...

mg



at hrs, mg



solve for ... then use the completed equation to find the time when mg

1.

A(t) = A(0) e^(kt)

A(0) =15

A(t) = 15 e^(kt)

A(2.5) = 25 =15 e^(2.5k)

5/3 = e^(2.5k)

ln(5/3) = 2.5 k

solve for k and you'll Have A(t)

Set A(t) = 45 and solve for t with ln

2. T(t) = se^(-kt) + 20

T(0) = 34 use this to solve for s

T(2) =31.7 use this to solve for k

You now have T(t) set this equal to 37 to determinine time of death

t will be negative the time before the body was first found

Many thanks to the both of you!