Light intensity(lumens) at a depth of x feet has the equation log I/12=-0.0125x
what depth will the light intensity be half that of the surface
at x=0, I = 12
so solve
log 6/12 = -x/8
log2 = x/8
x = 8log2
To find the depth at which the light intensity is half that of the surface, we can use the given equation:
log(I/12) = -0.0125x
First, let's solve for I, the light intensity at the given depth. We can rearrange the equation as follows:
I/12 = 10^(-0.0125x)
Next, multiply both sides of the equation by 12 to isolate I:
I = 12 * 10^(-0.0125x)
Finally, we can determine the depth x at which the light intensity is half that of the surface. This occurs when I is equal to half the surface light intensity, so I/2:
I/2 = 12 * 10^(-0.0125x)
Now, we need to solve for x. Divide both sides of the equation by 12:
(I/2) / 12 = 10^(-0.0125x)
(1/24) * I = 10^(-0.0125x)
Taking the logarithm of both sides, we get:
log((1/24) * I) = -0.0125x
Now, let's rearrange the equation to solve for x:
x = log((1/24) * I) / -0.0125
By substituting the value of I/2 for I, we can determine the depth at which the light intensity is half that of the surface.