can any 1 help me get tru this single problem ...please
any help will be greatly accepted

A thermometer reading 11°C is brought into a room with a constant temperature of 20°C. If the thermometer
reads 18°C after 3 minutes, what will it read after being in the room for 5 minutes? Assume the cooling follows
Newton's Law of Cooling:
U = T + (U0 - T)e^kt.

2. Use the curve given to you to find the value of the constants.

$U = T + (U_o - T)e^{kt}$

At time t = 3, the temperature is 18 C.

$18 = 20 + (11 - 20)e^{3k}$

Find the value of k.

Then, use the equation again with the value of k you obtained and t = 5. FInd the value of U.

What do you get?

3. $e^{kt}= left(e^k\right)^t$ so you really only need to find $e^k$, not k itself.

4. ## newton law of cooling

needs some assistance with this question please

A thermometer reading 11°C is brought into a room with a constant temperature of 20°C. If the thermometer
reads 18°C after 3 minutes, what will it read after being in the room for 5 minutes? Assume the cooling follows
Newton's Law of Cooling:
$
U = T + (U0 - T)e^{kt}
$

reach as far as this
$
18 = 20 + (11 - 20)e^{3k}
$

dont no if it is correct

5. I think you'll find that, with the way you've written the equation, k < 0. Try to solve for k. What do you get?

6. only reach as far as here

$18=20+(11-20)e^{3k}$
$-2=-9e^{3k}$
$\frac{2}{9}=e^{3k}$

wat to do from here

7. Ok. So far, so good. Now you need to "undo" the exponential function in order to get at the exponent. How do you "undo" an exponential?

8. not sure how thats done
can u break it down futher5 for me please

9. What is the function inverse of the exponential function? If I have the equation $y=e^{x},$ how could I solve for $x?$

10. is it this

$
ln (\frac{2}{9}) = ln (e)^{3k}
$

$
3k ln (e) = ln (\frac{2}{9})
$

$
3k ln (e) = ln (\frac{2}{9})
$

$
3k = -1.5040
$

$
k = -0.501359133
$

11. Well, I would write it this way (being careful with parentheses):

$\ln\left(\dfrac{2}{9}\right)=\ln\left(e^{3k}\right ).$

But that's definitely the right idea. Now what?

12. $
-1.5040774 = 3kln (e)
$

13. Keep going!

14. $
-1.5040774 = 3k

k = -0.501359133
$

15. So, k = -0.501359133. Now what?

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