Question

Okay, so
I worked out
17 = T(10) = 2 + 23e ^10k
15/23 = e^10k
k= 1/10ln(15/23)
k = - 0.043

But when I do this equation

17 = T(30) = 2 + 23e^30k
15/23 = e^30k
k = 1/30ln(15/23)
k = -0.142

But the answer is apparently 8.38?
Can someone please help.
I think I'm getting too tired and I can't pick up on my mistakes. =(

Answer 1

well of course if
T(t) = 2+23e^kt
T(10) will not equal T(30)
You sure they're both supposed to be 17?

So, what was the original problem?

Answer 2

Suppose that the temperature of the environment is 2 degrees and the initial temperature of the object is 25 degrees. After 10 minutes the temperature of the object is observed to be 17 degrees.

what is the temperature of the object after 30 minutes?
after how many minutes is the temperature of the object 4 degrees?

Answer 3

As I recall, you need Newton's law of cooling, which in this case would be

T(t) = 2+23e^(-kt)

where we try use a positive k.

T(10) = 17, so

2+23e^(-10k) = 17
k = 0.0427


and we have T(t) = 2+23e^(-.0427t)

So, after 30 minutes,

T(30) = 2+23e^(-.0427*30) = 8.388

When T=4, we have

2+23e^(-.0427t) = 4
t = 57.20

Answer 4

Ahhhhh! Okay awesome! Thank you!
Makes so much sense!