The light-gathering power of a telescope is directly related to the area of the telescope's primary mirror. a mirror with four times the diameter of another mirror collects how many times more light as the smaller mirror does in the same amount of time?

16 times

Explanation:

Generally, the light-gathering power of the mirror of a telescope is dependent on the area of the mirror. The area of the mirror is (π*d^2)/4. The variable 'd' is the diameter of the mirror. Therefore, if the diameter of A is four times the diameter of B, the light-gathering power of A will be (π*4^2)/4 while that of B will be (π*1^2)/4. This shows that A has 16 times that of B.

a and b sometimes have a positive value