Answer
$0.0088$
Work Step by Step
Let t be years after 2010.
$A=A_{0}e^{kt }$, and we are given:
$ A_{0 }=44.2\quad$ (for t=0 in 2010)
$A=62.9 \quad $when t=$40$, in 2050.
From this we find k:
$62.9=44.2e^{40k}\qquad/\div 44.2$
$\displaystyle \frac{62.9}{44.2}=e^{40k}\qquad$ ... apply ln( ) to both sides
$\ln \displaystyle \frac{62.9}{44.2} =40k\qquad /\div 40$
$k= \displaystyle \frac{\ln \frac{62.9}{44.2}}{40}\approx$0.00882053436557$\approx 0.0088$
