exponential growth and decay (1 Viewer)

[peppermint_stix]

ok i have a question here from ex. 19(b) fitzpatrick q. 18

sunlight transmitted into water loses intensity as it penetrates to greater depths according to the law I(d) = I(0)e^-kd
where I(d) is the intensity at depth d meters blow the surface, if
I(300) = 0.3 I(0) find:
a) the value of k
b) the depth at which the intensity would be decreased by one half.

plz helpppp!!! thanx

 

[Xayma]

a) at d=300, e^-300k=0.3
-300k ln e=ln 0.3
k=ln 0.3/-300
k=approx= 4.01x10^-3 (remember to use the full value for k in the question)

b) When the intensity is at half e^-kd=0.5
e^{-4.01x10^-3d}=0.5
-4.01x10^-3d ln e=ln 0.5
d=ln 0.5/(-4.01x10^-3)
d=172.71m (2 dp)