C3 exponential differentiation

i thaught it would be -60 not -6

I would appreciate some help with this question thanks!

Given that T is a measure of temperature in degrees C, t is the time in minutes and that T = 20 + 60e^-0.1t, t > or equal to 0

a) Find dT/dt
I worked it out and I got -6e^-0.1t

b) Find the value of T at which the temperature is decreasing at a rate of 1.8 degrees C per minute

I thought I would do -6e^-0.1t = 1.8
but then I am stuck, the answer I should get is 38

I answered this EXACT question a few hours ago.
I'll copy out my solution for you


your first answer is correct.

Then, find out the value for "t" and set the expression you found in a) equal to -1.8. (It's a decrease remember, so negative)

so basically -6e^0.1t = -1.8, take logs of both sides and solve for t.

Using your value of t (I get ~12.04 ish) substitute this into the original expression for T (not dT/dt).

So T = 60e^(-0.1 x 12.04) + 20

should give 38 *C

I answered this EXACT question a few hours ago.
I'll copy out my solution for you


your first answer is correct.

Then, find out the value for "t" and set the expression you found in a) equal to -1.8. (It's a decrease remember, so negative)

so basically -6e^0.1t = -1.8, take logs of both sides and solve for t.

Using your value of t (I get ~12.04 ish) substitute this into the original expression for T (not dT/dt).

So T = 60e^(-0.1 x 12.04) + 20

should give 38 *C

Ahhh brillaint, thanks! I was getting 12.04 but forgot to add it back in so I was doing again and again. Thank you!

glad I could help! Just thought it was such a coincidence when I saw the question lol, I have an interview tomorrow so I've been preparing for it and getting stressed out, haha

oooh, interview for what if you don't mind me asking?

it was for civil engineering at imperial
fingers crossed it went well, the interview wasn't as daunting as I thought it would be and the interviewer was lovely! but I don't want to think about it too much in case I don't get an offer on ucas! Loved the place though!

Oh brillaint! I am sure you did great, Good luck with that

Thanks!
are you applying this year?

Yupp , I've applied for medicine at Newcastle, Leicester, Aberdeen, Glasgow and Chemical Engineering at UCL. I still haven't got any interviews so am still waiting

Ooooh of course, just realised it says so in your sig! lol, good luck with them all though