Question

Question on exponents

Answer 1

An oven has a theoretical maximum temperature of 500°C. The temperature of the room is 20°C. Because of radiation losses, when the oven is switched on its temperature T increases each minute by 10% of the difference between its temperature and the theoretical maximum; that is, (500 − T) decreases by 10% each minute.

Set up a model of the oven temperature m minutes after it is switched on.

Question is confusing me so much

Answer 2

is it the temperature inside the oven that is increasing or its film surface outside temperature?

Answer 3

I believe the temperature inside the oven that is increasing @chris00

Answer 4

what have you been studying in this subject?
have you learnt first order equation? differential equation? etc..or not?

Answer 5

We've done differential, this is on the "indices and indices laws" section, with exponential growth and decay

Answer 6

yeah right

Answer 7

its been ages since ive done this um..

Answer 8

have you learnt logistic functions?

Answer 9

Yes

Answer 10

im unsure of the quesiton, you say there is a theortical maximum of 500 degrees right? now, the temperature of the oven increases by 0.1(500-T) each minute, yet the theortical maximum drops by 10% of (500-T)?

yes, theortical max temperature would drop because of radiation heat transfer, convection heat transfer etc but i'm unsure how we could model this with such info

Answer 11

It is just saying the rate is dropping , not the max temp.

Answer 12

perhaps solve \[\frac{ dT }{ dt }=0.1(500-T)\]

Answer 13

i'm only throwing ideas here

Answer 14

The question is really confusingly worded. Will giving the equation help us understand what we need to do?

Answer 15

yes, solving the differential equation sounds good.

Answer 16

do you know how to solve the differential equation @Ahsome

Answer 17

i think thats a logarithm function you learn in final year in high school...

Answer 18

Here is a plot

Answer 19

i was so interested in this question because i was like first order system! thats what i'm learning now in process control

Answer 20

Sorry! Had to have dinne. This is the answer
\[T=500-480\times0.9^m\]

Answer 21

correct, although we tend to use the exponential function in the equation.

Answer 22

\[T(t)=500-480e ^{-0.1t}\]

Answer 23

so by simply solving the differential equation, we can get to this solution

Answer 24

can you do this?

Answer 25

We haven't used Euler's number yet @chris00

Answer 26

thats how you solve the differential function of \[\frac{ dT }{ dt }=0.1(500-T)\]

Answer 27

have you learnt how to solve differential equations?

Answer 28

We don't need to differentiate the equation, we just need to come up with it @chris00 :)
I just have no idea how to make that equation from the question itself

Answer 29

well simply temerpature is affected by the time right? We say that the temerpature changes with resepct to time. Hence, temperature being the rate of change with resepect to time.

Answer 30

and since the question says that the temperature increases by 10% of (500-T) per MINUTE, then this is a rate

Answer 31

we express rates as a differential function, i.e\[\frac{ dT }{ dt}\]

Answer 32

this simply means, the change in temperature with respect to the change in time.

Answer 33

and since we know that the the temperature changes by 10% of (500-T) with respect to time (in minute basis) then, we simply equal this to the differential term

Answer 34

i.e \[\frac{ dT }{ dt}=0.1(500-T)\]

Answer 35

0.1 is simply a decimal form which represents 10% right?

Answer 36

Yup

Answer 37

have you sort of grasped this concept yet?

Answer 38

I get that. But I am confused where the 480 comes into play :/

Answer 39

its comes out when you solve it...

Answer 40

\[\frac{ dT }{ dt }=0.1(500-T)\]
\[\frac{ dT }{ 500-T }=0.1dt\]

Answer 41

\[\int\limits_{}^{}\frac{ dT }{ 500-T }=\int\limits_{}^{}0.1dt\]

Answer 42

remember separable differential equations?

Answer 43

@Ahsome

Answer 44

We haven't done that. This is meant to be WAY simpler than th

Answer 45

Than that* @chris00

Answer 46

yea interesting :/

Answer 47

im not sure if i can help you then :/