A company determines that its marginal revenue per day is given by R'(t), where Rit) is the total accumulated revenue, in dollars, on the ith day. The company's marginal cost per day is given by C'(1), where C(1) is the total accumulated cost, in dollars, on the fth day. R'() = 80e ', R(0) = 0: C'(t) = 80 - 0.at, c(0) = 0 a) Find the total profit P(T) from t= 0 to t= 10 (the first 10 days). P(T) =RIT)-C() =J .[R'()-c'(] The total profit is $ - (Round to the nearest cent as needed.) company determines that its weekly online sales, S(1), in hundreds of dollars, it weeks after online sales began can be estimated by the equation below. Find the average weekly sales of the first 3 weeks after online sales began. The average weekly sales amount is $1. (Round to the nearest cent as needed.) In a memory experiment, Alice is able to memorize words at a rate given by m'(t) = - 0.0031" + 0.5t. In the same memory experiment, Ben is able to memorize words at the rate given by M'(1) = = 0.009t + 0.5L. a) Who has the higher rate of memorization? Alice O Ben b) How many more words does that person memorize from = 0 to t= 10 (during the first 10 minutes of the experiment)? more words (Simplify your answer.) The concentration, C, of phenylbutazone, in micrograms per milliliter (up/mL), in the plasma of a calf injected with this anti-inflammatory agent is given approximately by C(1) = 42.89 -0:010511, where t is the number of hours after the Injection and Ost5110. a) Given that the model is accurate for Osts 110, what is the initial dosage? bi What is the average amount of phenylbutazone in the calf's body for the time between 10 and 110 hours? BD 120 a) The initial dosage is pgimL. (Type an integer or a decimal.) Suppose the temperature in degrees Celsius over an 8-hour period is given by T() = -1 +71 +32. U *) Find the average temperature. bj Find the minimum temperature. c) Find the maximum temperature. ") The average temperature is degrees. (Type an integer or a decimal. Round to one decimal place as needed.)