after t months on the job a postal clerk cn sort Q(t)=700-400e^-0.5t letters per hour. Wht is the average rate at which the clerk sorts mail during the first 3 months on the job.
What is the average rte t which the clerk sorts mail during the first 3 months on the job?
What is the average rate during the next 3 months?
To find the average rate at which the clerk sorts mail during the first 3 months on the job, we need to calculate the average value of the sorting rate function Q(t) over that period.
The average value of a function over an interval [a, b] is given by the formula:
Average value = (1 / (b - a)) * ∫[a to b] f(t) dt
In this case, a = 0 (representing the start of the job) and b = 3 (representing the end of the first 3 months). The function is Q(t) = 700 - 400e^(-0.5t).
To find the average rate during the first 3 months, we need to calculate the integral of Q(t) over the interval [0, 3].
Average rate = (1 / (3 - 0)) * ∫[0 to 3] (700 - 400e^(-0.5t)) dt
Evaluating this integral will give us the average rate at which the clerk sorted mail during the first 3 months on the job.
Similarly, to find the average rate during the next 3 months, we need to calculate the average value of Q(t) over the interval [3, 6]. Using the same formula as before, the integral would be evaluated over the interval [3, 6].