Summation Problems: Solve Delta ti * T(Delta ti) for Age in Days

[Cokemaster]

Hello,

Some of you may know this equation and I need help solving it.
Delta t_i is the time in days at a certain temperature (0 - 80).
T(Delta t_i) is the temperature during Delta t_i.

The answer is supposed to be an age in days but my tries have given me answers that are below 1, which doesn't make any sense. Can someone please try to open this up for me?

 

[I like Serena]

Hello,

Some of you may know this equation and I need help solving it.
Delta t_i is the time in days at a certain temperature (0 - 80).
T(Delta t_i) is the temperature during Delta t_i.

The answer is supposed to be an age in days but my tries have given me answers that are below 1, which doesn't make any sense. Can someone please try to open this up for me?

Hi Cer! Welcome to MHB! :)

Mmm... let's try $T(\Delta t_i)=27^\circ \text C$ with $\Delta t_i=10 \text{ days}$.

Then we get:
$$e^{-(4000/300-13.65)} \cdot \Delta t_i= e^{0.32} \cdot 10 \approx 13.8 \text{ days}$$

What is the problem?