1. An exposure control apparatus for performing exposure control for a camera mounted on a vehicle in accordance with brightness of a recognition area set in an image ahead of the vehicle taken by the camera, the exposure control apparatus comprising: a measuring unit measuring brightness of a photometric area showing a landscape more distant from the vehicle than a landscape shown by the recognition area in each of images successively taken by the camera; a detection unit detecting brightness variation with time of the photometric area based on measurement results by the measuring unit for images taken by the camera at different times; and a control unit configured to predict a timing at which the brightness of the recognition area changes based on the brightness variation with time of the photometric area detected by the detection unit, and perform exposure control of the camera at the predicted timing; wherein the control unit is configured to estimate based on a speed of the vehicle, as a next-time recognition area, an image area assumed to be included in the recognition area of an image taken by the camera next time, and determine whether or not the brightness of the recognition area will change at the time when the camera takes an image next time based on brightness variation with time of the next-time recognition area detected by the detection unit; wherein the detection unit is configured to detect an amount of brightness variation with time of the brightness of the next-time recognition area based on the measurement results by the measuring unit for images taken by the camera at different times, and the control unit is configured to determine whether or not the brightness of the recognition area will change at the time when the camera takes an image next time by comparing the amount of brightness variation with time of the next-time recognition area detected by the detection unit with a determination threshold; wherein the control unit is configured to make a determination whether or not the brightness of the recognition area will change when the camera takes an image next time, calculate an exposure control value used to control exposure of the camera when the determination is affirmative, and set, as the exposure control value for the time when the camera takes an image next time, the exposure control value previously calculated when the determination is negative; wherein the photometric area is an area in which the own vehicle is assumed to run at the next image-taking cycle, and wherein the brightness variation with time of the next-time recognition area is the difference between the brightness measured when an exposure control value was changed last time and the brightness measured this time.