Answer
a. 7.87 lumens
b. at 86.6 ft
Work Step by Step
a.
insert t=30 and calculate I:
$I=10e^{-0.008(30)}=10e^{-0.24}\approx 7.87$.
At 30 ft the intensity is 7.87 lumens.
b.
Find t when I =5
$5=10e^{-0.008x} \qquad .../\div 10$
$e^{-0.008x}=\displaystyle \frac{1}{2} \qquad$ ... apply $\ln$() to both sides
$-0.008x=\displaystyle \ln(\frac{1}{2}) \qquad .../\div(-0.008)$
$x=\displaystyle \frac{\ln0.5}{-0.008}\approx 86.6$.
So the intensity drops to 25 lumens at 86.6 ft.
