What is the time constant of the cooled steel billet?

[Northbysouth]

16. As part of a heat-treating process, an alloy-steel billet, initially at 1032°F, is cooled in a 32°F air stream. The temperature history of the billet is shown in the figure at right.
What is the time constant τ for the cooling process?

I have attached an image of the question.

I have the equation:

T = T_∞ + (T_i-T_∞)e^-t/τ

I know that:

T_∞ = 32°F

T_i = 1023°F

But I'm a little uncertain about the time. If I take the max temperature value, 1032°F, and multiply this by 0.368, would this give me the time and temperature at one time constant?

 

[NascentOxygen]

Exponential decay is based on the difference value, the difference between where it is now and where it is headed finally. In one time constant it closes the distance by 63.2% leaving 36.8% of that difference to go.