The percent moisture content of hardwood lumber drying in McTaggart Plywood’s kiln follows an exponential decay function with the lumber losing half of its percent moisture content in 56.0 hours. If the initial moisture content of a new batch of hardwood lumber is 58.5% when placed in the kiln:

- What will the moisture content of this lumber be after 100 hours?
- How long will it take for the moisture content of this lumber to reach 8.0%?

Solution:

The percent moisture content, *m*, follows an
exponential decay function as follows:

where:

*m*is the moisture content at time*t**m0*is the moisture content at time*t*= 0*k*is the decay constant.

The first thing we should do is find the value of
*k*:

We know that if *m0* = 1, then *m* = 0.5, when *t* = 56.0

So, 0.5=(1)e-k(56.0) and taking the natural log of both sides, we get

ln(0.5)/ 56.0 = -*k*, and *k* is approximately 0.01238

Therefore

(a) Using , find *m*, if *m0* = 58.5% and *t* = 100.0 hours.

After 100.0 hours, the moisture content of the lumber will be approximately 17.0%.

(b) Using , find *t*, if *m0* = 58.5% and *m *= 8.0% hours.

, and taking the natural log of both sides, we get

ln(8.0) – ln(58.5) = -0.01238 *t*,

and

*t* = -1.989585/-0.01238 = 160.7096

It will take about 161 hours for the moisture content of the lumber to reduce to 8.0%.

This could also be estimated from a graph of the moisture content curve, plotted using the equation
with *m0*=58.5.