Answer
$-0.0069$
Work Step by Step
Let t be years after 2010.
$A=A_{0}e^{kt }$, and we are given:
$ A_{0 }=7.1\quad$ (for t=0 in 2010)
$A=5.4 \quad $when t=$40$, in 2050.
From this we find k:
$5.4=7.1e^{40k}\qquad/\div 7.1$
$\displaystyle \frac{5.4}{7.1}=e^{40k}\qquad$ ... apply ln( ) to both sides
$\ln \displaystyle \frac{5.4}{7.1} =40k\qquad /\div 40$
$k= \displaystyle \frac{\ln \frac{5.4}{7.1}}{40}\approx$-0.00684239576193$\approx-0.0069$
