The aperture setting, or f-stop, of a digital camera controls the amount of light exposure on the sensor. Each higher number of the f-stop doubles the amount of light exposure. The formula n=log_2(1/p) represents the change in the number, n, of the f-stop needed, where p is the amount of light exposed on the sensor.

a) a photographer wishes to change the f-stop to accomodate a cloudy day in which only 1/4 of the sunlight is available. How many f-stops does the setting need to be moved?

My answer:
2 (which is correct)

b) if the photographer decreases the f-stop by four settings, what fraction of the light is allowed to fall on the sensor?

I need help on part b. My attempt is this:
-4p=log_2(1/p)
then I solved for p, and got -1/2 but it is wrong.

To find the fraction of light allowed to fall on the sensor when the f-stop is decreased by four settings, we can use the formula:

n = log2(1/p)

In this case, since we are decreasing the f-stop by four settings, the value of n will be -4. We need to solve for p, which represents the fraction of light exposed on the sensor.

Thus, the equation becomes:

-4 = log2(1/p)

To isolate p, we need to use logarithmic properties. In this case, we can rewrite the equation as an exponential equation:

2^-4 = 1/p

Now, we can simplify further:

1/2^4 = 1/p

1/16 = 1/p

To solve for p, we can take the reciprocal of both sides:

p = 16

Therefore, when the f-stop is decreased by four settings, the fraction of light allowed to fall on the sensor is 1/16.