Derivatives Question - temperature as a funtion of time

[livestrong136]

Derivatives Question -- temperature as a funtion of time

1. When a certain object is placed in an oven at 540°C, its temperature T(t) rises according to the equation T(t) = 540(1 – e–0.1t), where tis the elapsed time (in minutes). What is the temperature after 10 minutes and how quickly is it rising at this time?

My Work: Temp after t minutes is given. Just plug in t = 10 mins in the equation ie T = 540(1-1/e)
rate of change is dT/dt (at t = 10) = 54/e

I said the rate of change at t=10 is 54/e. 54/e is incorrect. not sure why I was dividing, in this question we need to show how you got the derivative to get full marks. Can someone help me with this.

 

[tiny-tim]

hi livestrong136!

(try using the X² button just above the Reply box )

T = 540(1 – e^–0.1t)

so what is dT/dt ?

(use the chain rule)