differentiation of T = a + be^kt with respect to "t" (a, b, k constants)

[bobman]

Hello everyone

Can someone help me on this problem as I am having a hard time getting to understand
the subject. I would love to get a full explanation as my tutors are rubbish at really giving an adequate explanation:

I am asked to differentiate with respect to 't':
T=a+be^kt
where T = temperature
t= time
a, b and k are constants
with values a= 20 deg c
b= 80 deg c
k= 2.6 x 10^-4 s^-1

Please help!
many thanks

Bobman

 

[stapel]

Can someone help me on this problem as I am having a hard time getting to understand the subject.

Okay; so you're asking for lesson instruction.

I am asked to differentiate with respect to 't': T=a+be^kt
T: temperature
t: time
a, b and k are constants, with values a= 20 deg C, b= 80 deg C, and k= 2.6 x 10^-4 s^-1

Okay, so you started with the algebra of plug-n-chug:

. . . . .\(\displaystyle T(t)\, =\, 20\, +\, 80\, e^{(2.6\, \times\, 10^{-4})\, t}\)

You'll need to apply the derivative rules for constants, for products, and for exponentials.

Once you have studied the lessons above, please attempt the exercise. If you get stuck, please reply showing all of your thoughts and efforts so far. Thank you!