what is the rate of change in temperature??

Question

1.) find the instantaneous rate of change in temperature with respect to time.

T(t) = (4t) / (t^2+1) + 98.6


2.) find the rate of change at t = 2 hours

Answer 1

The instantaneous rate of change is given by the derivative of T(t) with respect to t.

Solve that equation with t=2 to find the rate of change at that particular instant.

Answer 2

First use the quotient rule to find the derivitave:
T'(t)=[[(t^2+1)(4)-(4t)(2t)]/(t^2+1)^2]+0

simplifiying we get:
[4t^2+4-8t^2]/(t^2+1)^2
=-4t^2/(t^2+1)^2

now substitute 2 for t and solve

Hope this helps!

Answer 3

1) T(t) = (4t) / (t^2 + 1) + 98.6
T'(t) ={ 4[(t^2 + 1) + 98.6] - (2t.4t)} / { (t^2+1) +9.8}^2
T'(t) = ( 4t^2 + 4 + 394.4 - 4t^2) / [(t^2 + 1) + 9.8]^2
T'(t) = 398.4 / [ (t^2 + 1) + 9.8]^2

2) at t= 2hrs
T'(2) = 398.4 / [ (2^2 + 1) + 9.8]
T'(2) = 398.4 /14.8
= 26.9