The photic zone in the ocean is the zone from the surface down to a depth where only about 1% of surface light penetrates. The intensity of light in the ocean as a function of depth x (in meters) is given by the Beer-Lambert Model I(x)=C * a^x , 0

Question

The photic zone in the ocean is the zone from the surface down to a depth where only about 1% of surface light penetrates. The intensity of light in the ocean as a function of depth x (in meters) is given by the Beer-Lambert Model I(x)=C * a^x , 0<a<1, and C is the intensity at the surface. In one region, the depth of the photic zone is about 16 meters. Find the value of the constant a for this region.

anonymous · Answer

You need to know the value of a.

anonymous · Answer

That's what the question is asking for. It wants you to find the value of a.

anonymous · Answer

Oh, wait. It's asking you to solve for a. Well, then you need to know the value of C.

anonymous · Answer

I replaced something with C because I couldn't figure out how to type it. Here's the real equation: $$I(x)=I{0}timesa ^{16}$$

anonymous · Answer

C is actually I with a small 0 subtext next to it.

anonymous · Answer

Do you know the value of
$$I_0$$

anonymous · Answer

No.

anonymous · Answer

This problem sucks.

anonymous · Answer

Oh nevermind. Just use:
.1 = 1*a^16

asnaseer · Answer

ok, so you are given:$$I(x)=I_0a^x$$and you are told that:$$I(16)=0.01$$therefore:$$0.01=I_0a^{16}$$therefore:$$a^{16}=\frac{0.01}{I_0}$$then just take the sixteenth root of both sides to find 'a'.

anonymous · Answer

Ah yes. 0.01, indeed.

anonymous · Answer

Yes! Thank you both :)

asnaseer · Answer

yw