Answer
$0.0088$
Work Step by Step
Exponential growth model $: \quad A= A_{0}e^{kt}$.
If $ k \gt 0$, the function models the amount of a growing entity.
$ A_{0}$ is the original amount, or size, of the growing entity at time t = 0,
$ A $ is the amount at time $ t $, and
$ k $ is a constant representing the growth rate.
If k is negative, the model is an exponential decay model.
----
Model: $ A=A_{0}e^{kt}$
$ t=0$ for the year $2010.$
Unknown: $ k $, when $ A_{0}=44.2, A=62.9, t=40,$
$ 62.9=44.2e^{k\cdot 40}\qquad $... /$\div 44.2$
$ 1.423\approx e^{k\cdot 40}\qquad $... $/\ln(...)$
$ 0.3528=40k\qquad $... /$\div 40$
$ k\approx 0.0088$
