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Ahsome
 one year ago
Question on exponents
Ahsome
 one year ago
Question on exponents

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ahsome
 one year ago
Best ResponseYou've already chosen the best response.0An 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it the temperature inside the oven that is increasing or its film surface outside temperature?

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0I believe the temperature inside the oven that is increasing @chris00

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what have you been studying in this subject? have you learnt first order equation? differential equation? etc..or not?

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0We've done differential, this is on the "indices and indices laws" section, with exponential growth and decay

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its been ages since ive done this um..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0have you learnt logistic functions?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im 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(500T) each minute, yet the theortical maximum drops by 10% of (500T)? 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

phi
 one year ago
Best ResponseYou've already chosen the best response.0It is just saying the rate is dropping , not the max temp.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0perhaps solve \[\frac{ dT }{ dt }=0.1(500T)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i'm only throwing ideas here

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0The question is really confusingly worded. Will giving the equation help us understand what we need to do?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, solving the differential equation sounds good.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know how to solve the differential equation @Ahsome

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think thats a logarithm function you learn in final year in high school...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i was so interested in this question because i was like first order system! thats what i'm learning now in process control

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0Sorry! Had to have dinne. This is the answer \[T=500480\times0.9^m\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0correct, although we tend to use the exponential function in the equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[T(t)=500480e ^{0.1t}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so by simply solving the differential equation, we can get to this solution

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0We haven't used Euler's number yet @chris00

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats how you solve the differential function of \[\frac{ dT }{ dt }=0.1(500T)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0have you learnt how to solve differential equations?

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0We 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and since the question says that the temperature increases by 10% of (500T) per MINUTE, then this is a rate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we express rates as a differential function, i.e\[\frac{ dT }{ dt}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this simply means, the change in temperature with respect to the change in time.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and since we know that the the temperature changes by 10% of (500T) with respect to time (in minute basis) then, we simply equal this to the differential term

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i.e \[\frac{ dT }{ dt}=0.1(500T)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00.1 is simply a decimal form which represents 10% right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0have you sort of grasped this concept yet?

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0I get that. But I am confused where the 480 comes into play :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its comes out when you solve it...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dT }{ dt }=0.1(500T)\] \[\frac{ dT }{ 500T }=0.1dt\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}\frac{ dT }{ 500T }=\int\limits_{}^{}0.1dt\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0remember separable differential equations?

ahsome
 one year ago
Best ResponseYou've already chosen the best response.0We haven't done that. This is meant to be WAY simpler than th

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not sure if i can help you then :/
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