Question

Medal ofcourse.

Jodi pours herself a cold soda that has an initial temperature of 38 F and immediately went outside to sunbathe where the temperature was a steady 95 F. After 7 minutes the temperature of the soda was 46 F. Jodi had to run back into the house to answer the phone. What is the expected temperature of the soda after an additional 10 minutes?

Answer 1

easy way or hard way?

Answer 2

ah hell lets to it the easy way because... it is easy

Answer 3

\[T(t)=S+(T _{0}-S)e ^{kt}\]

Answer 4

you can use an exponential model, you are given two points

Answer 5

46=95+(-57)e^7k

Answer 6

that is the ridiculous way lets make it simple
start with the temp at 95 and the outside temp at 38
we work with the differnece in temps, which is \(95-38=57\)

Answer 7

ok

Answer 8

I was using newtons law of cooling

Answer 9

in ten minutes the difference in temp is \(95-46=49\)
yeah i know

Answer 10

no starts with 38

Answer 11

it starts cold

Answer 12

ok lets back up

Answer 13

outside temp is 95
beer is 38
difference is \(95-38=57\)

Answer 14

i did

y = 38 * e^(k*t)

46 = 38 * e^(k*t) , solve for k

Answer 15

in ten minutes, outside temp is still 95, beer is 46, difference is \(95-46=57\)

Answer 16

sattelite, u r the only person i know that can turn soda into beer. :)

Answer 17

I want to see what ur trying to do.

Answer 18

ratio is \[\frac{57}{46}\] in ten minutes
in another ten minutes it will be \((\frac{57}{46})^2\)

Answer 19

57/46 in 7 mins

Answer 20

take \[57\times \left(\frac{57}{46}\right)^2\] to get the new difference

Answer 21

I got y = 38 * e^( .0191 * t )

Answer 22

then subtract that from \(95\)

Answer 23

@perl the 38 is wrong
you work with the differences in the temperatures, not the actual temperature

Answer 24

i had said 10 minutes. i meant 7 minutes. its alright if u want to stop working on the problem. I can work it out by myself.

Answer 25

ok if it is 7 minutes, then we have to do something different

Answer 26

After 7* minutes the temperature of the soda was 46 F.

Answer 27

that's why i did this to solve for k:
46=95+(-57)e^7k

Answer 28

ok

Answer 29

so...
-49=-57e^7k

Answer 30

49/57=e^7k
ln(49/57)=7k

Answer 31

[ln(49/57)]/7=k

Answer 32

ok i was using the wrong model.

Answer 33

looks like you got it to me, once you have the model, replace \(t\) by \(17\)

Answer 34

temperature change is proportional to the difference in temp. not the actual temperature?

Answer 35

k=-0.02160442424

Answer 36

@perl yes, the difference decays to zero

Answer 37

T(17)=95+(-57)e^17k
T(17)=95-39.4792830925

Answer 38

T(17)=55.5207169075

Answer 39

you changed your question to 7 minutes

Answer 40

you can edit your question

Answer 41

ok

Answer 42

Jodi pours herself a cold soda that has an initial temperature of 38 F and immediately went outside to sunbathe where the temperature was a steady 95 F. After *7* minutes the temperature of the soda was 46 F. Jodi had to run back into the house to answer the phone. What is the expected temperature of the soda after an additional 10 minutes?

Answer 43

56 is not workingn -_-

Answer 44

one sec, checking

Answer 45

T(t) = Ta + ( To - Ta) e^(-kt)

Answer 46

T(t) = 95 + (38 - 95) e^(-kt)

Answer 47

i dont have -kt in the equation i was given

Answer 48

but it seems that it wont matter

Answer 49

right, it wont matter

Answer 50

k is usually considered positive

Answer 51

so in decay problems, we put a negative in front of k

Answer 52

ok

Answer 53

did you get
k = ln (49/57) / 7

Answer 54

T(t) = 95 -57 e^(-.021604 * t )

Answer 55

T(17) = 55.5

Answer 56

I had to round to the whole for the previous questions so I did the same here. I trid 56 snd 55. It turs out it wanted it rounded to the tenth. 55.5 is CORRECT!

Answer 57

Thanks so much @perl . Could u medal @satellite73 and ill medal u.

Answer 58

sure

Answer 59

I could have just solved this myself but I came here. The power of laziness. :)

Answer 60

:D

Answer 61

XD