 Solution

A one-unit increase in testosterone concentration, here $1ng/dL$, multiplies the expected offspring count by $\boxed{e^{{\beta }_T}}$ under the Poisson regression with a log link. Thus the exact percentage change in the conditional mean is $\boxed{100(e^{{\beta }_T}-1)\%}$. The regression coefficient ${\beta }_T$ itself is the change in the logarithm of the expected count, not an additive change in offspring number.