# Thread: VERY hard differentiation analysis questions

1. ## VERY hard differentiation analysis questions

Equation is:
T represents temperature of water.
T=Me-kt , where t is equal or greater than 0. t represents time.
M= 55 and k = 0.0141 approx.

Question:
The time at which water is cooling at 1degree/second is -18.03, and hence is a puzzling answer( since time cannot take a negative value) . Explain why the answer is puzzling in terms of the student's model(equation)

-----------------

If 55loge (0.986) = -0.7754 approx.

and T=55eloge (0.986t)

Show algebraic steps to obtain approximation and state value of approximation to 2 decimal places

2. Originally Posted by delicate_tears
Equation is:
T represents temperature of water.
T=Me-kt , where t is equal or greater than 0. t represents time.
M= 55 and k = 0.0141 approx.

Question:
The time at which water is cooling at 1degree/second is -18.03, and hence is a puzzling answer( since time cannot take a negative value) . Explain why the answer is puzzling in terms of the student's model(equation)

-----------------

If 55loge (0.986) = -0.7754 approx.

and T=55eloge (0.986t)

Show algebraic steps to obtain approximation and state value of approximation to 2 decimal places
I suppose you mean $\displaystyle T = Me^{-kt}$ ???

$\displaystyle T' = -kMe^{-kt}$

at $\displaystyle t = 0$, $\displaystyle T' = -kM = -.7755 \, \frac{deg}{sec}$

since $\displaystyle T'' = k^2Me^{-kt} > 0$ for all $\displaystyle t \ge 0$ , the value of $\displaystyle T'$ will increase over time.

3. Originally Posted by delicate_tears
Equation is:
T represents temperature of water.
T=Me-kt , where t is equal or greater than 0. t represents time.
M= 55 and k = 0.0141 approx.

Question:
The time at which water is cooling at 1degree/second is -18.03, and hence is a puzzling answer( since time cannot take a negative value) .

Why can't t take a negative value? t= 0 must refer to some specific point in time. t negative refers to time before that.

Explain why the answer is puzzling in terms of the student's model(equation)

-----------------
If 55loge (0.986) = -0.7754 approx.

and T=55eloge (0.986t)

Show algebraic steps to obtain approximation and state value of approximation to 2 decimal places