Final answer:
The correct choice is B. Increase kilovolts peak (kVp) by 15% to double the image density without significantly increasing the patient's dose.
Step-by-step explanation:
If a radiographer wants to double the image density without doubling the patient's dose, increasing the kilovolts peak (kVp) by 15% is the action that should be taken. This is because increasing the kVp increases the energy of the X-rays and thereby increases the penetrating power of the X-ray beam. This results in a denser image without increasing the patient's exposure to radiation as much as doubling the milliampere-seconds (mAs) would. Essentially, a 15% increase in kVp can potentially double the density of an X-ray image without a corresponding increase in dose.