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# Calculus - rates of change

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1. Hi,

I was just wondering if the way I worked out this question is correct.

Basically I subbed in 4 into the dT/dt equation and then the answer I got from that I added it to -7. Is this correct ?

Thanks
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2. (Original post by Olive123)
Hi,

I was just wondering if the way I worked out this question is correct.

Basically I subbed in 4 into the dT/dt equation and then the answer I got from that I added it to -7. Is this correct ?

Thanks
They are asking for the temperature at the end of 4 hours. Subbing 4 into will give you the rate at which the temperature is increasing with time.

To get back to an equation involving the temperature, what would you do to the equation? A hint is in the spoiler.
Spoiler:
Show
Hint: Try integrating the differential equation to form a linear equation involving T and t.
3. (Original post by Dapperblook22)
They are asking for the temperature at the end of 4 hours. Subbing 4 into will give you the rate at which the temperature is increasing with time.

To get back to an equation involving the temperature, what would you do to the equation? A hint is in the spoiler.
Spoiler:
Show
Hint: Try integrating the differential equation to form a linear equation involving T and t.

So after integrating should I sub in T=-7degrees to get the constant?

Should I then use the temp equation I got from integrating and sub in t=4 to find the temp at the end of 4 hours ?
4. (Original post by Olive123)
So after integrating should I sub in T=-7degrees to get the constant?

Should I then use the temp equation I got from integrating and sub in t=4 to find the temp at the end of 4 hours ?
Yes, you would sub in T = -7 and t = 0 (as the temperature is initally -7 degrees), and then use the equation you got from integrating.
5. (Original post by Dapperblook22)
Yes, you would sub in T = -7 and t = 0 (as the temperature is initally -7 degrees), and then use the equation you got from integrating.
Thanks a bunch
6. Forget the question! Look at the hyperbolas the pixels on your screen are making
7. (Original post by Sinfire)
Forget the question! Look at the hyperbolas the pixels on your screen are making
Nice observation ha
8. Yes as long as your units of time are correct. As T(t) is the form of the equation f(x) I.e. The function of x will produce a temperature which is proportional to e to the power of the time taken including any coefficients.

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Updated: August 11, 2016
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