Answer:
57
Explanation:
To find the total number of vehicles passing through the traffic light at the end of 7 hours, we need to use the formula for exponential decay:
N(t) = N0 * e^(-rt)
where N(t) is the number of vehicles at time t, N0 is the initial number of vehicles, r is the decay rate (in this case, 5% per hour), and t is the time elapsed.
We know that the initial number of vehicles is 82, so N0 = 82. The decay rate is 5% per hour, or r = 0.05. We want to find the number of vehicles after 7 hours, so t = 7.
Plugging these values into the formula, we get:
N(7) = 82 * e^(-0.05*7)
N(7) = 82 * e^(-0.35)
N(7) = 82 * 0.704
N(7) = 57.728
Therefore, at the end of 7 hours, we can estimate that the total number of vehicles passing through the traffic light will be about 57.728.