Question

Currently, the number of vehicles passing through a traffic light is 82. It is estimated that the number of vehicles passing through the traffic light will decrease by 5% each hour. Find the total number of vehicles passing through the traffic light at the end of 7 hours.

Select the correct answer below:
434
470
488
495

Answer 1

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.