A star is being observed with an 8 bit charge-coupled device (CCD) that has a central pixel value of 82 counts when the exposure time is 10 seconds. What would the central pixel value be if the exposure time were 25 seconds? Why?
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A charge-coupled device (CCD) is a computer chip attached to a telescope that "functions as a camera" and can be used by astronomers to photograph stars (Astronomy Education at the University of Nebraska-Lincoln, "Properties of CCDs"). CCDs are especially useful for photographing variable stars in order to plot the changes in brightness. CCDs have many effective mechanisms for detecting light by counting quanta, or small amounts, of light, which we call photons.
The CCDs sense the photons through electrical charges as they hit the pixels, or locations, on the chip. However, CCDs can only count up to a certain maximum number of photons, and if more than the maximum number of photons hit one pixel, then the pixel becomes what we call "saturated," and the image of the star will appear with streaks, which we call "blooming." To prevent saturation, we have to adjust the CCD's bit depth b, which represents the "number of computer bits (0 or 1) that can be used to store the value of each pixel" ("Properties of CCDs"). We must also adjust exposure time along with bit depth to prevent saturation.
In your problem, if we begin with an 8 bit depth and an exposure time of 10 seconds, then the number of photons that hit the central pixel is roughly 82 counts. If we increase the exposure time to 25 seconds, we are more than doubling the exposure time, so the number of photons that will hit the central pixel will also more than double, which would be approximately 180 counts. We can also use the CCD simulator on the Astronomy Education at the University of Nebraska-Lincoln website to check our answer. Using the CCD simulator, we see that the number of counts is roughly between 160 to 180 ("Properties of CCDs").
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