Answer
$0.0174$
Work Step by Step
Let t be years after 2010.
$A=A_{0}e^{kt }$, and we are given:
$ A_{0 }=21.3\quad$ (for t=0 in 2010)
$A=42.7 \quad $when t=$40$, in 2050.
From this we find k:
$42.7=21.3e^{40k}\qquad/\div 21.3$
$\displaystyle \frac{42.7}{21.3}=e^{40k}\qquad$ ... apply ln( ) to both sides
$\ln \displaystyle \frac{42.7}{21.3} =40k\qquad /\div 40$
$k= \displaystyle \frac{\ln \frac{42.7}{21.3}}{40}\approx$0.017387296188$\approx 0.0174$
