Question

HW4 2: Problem 10 Previous Problem List Next (1 point) Oil leaks from a tank. At hour t = 0 there are 220 gallons of oil in the tank. Each hour after that, 7% of the oil leaks out. (a) What percent of the original 220 gallons has leaked out after 11 hours? (b) If Q(t) = Qoek is the quantity of oil remaining after t hours, find the value of k. k = (c) What does k tell you about the leaking oil? Select all that apply if more than one statement is true A. It tells by what percent of oil decays each hour. B. Because it is negative, we know the amount of oil in the tank is decreasing. C. Because it is less than one, we know the amount of oil in the tank is decreasing D. It gives the continuous hourly rate at which oil is leaking. E. It is the amount that the oil that leaks out each second. F. It tells what percent of oil remains after each hour. G. None of the above Note: You can earn partial credit on this problem.

Answer 1

Cliven bil too is 220 gallons leaks from tank at ie (666) = 220) (a) for 866), with the decay of al. per each hour, then the remain 't hours as act) - Q6) [ 1 2 ] Here Qc0)=220; n=71. u t= 11 hours QUID - 220[1- too]" (Qori) = 99.022 Given Qet) = Qoekt We know that QCM = 99.022; when tall; 20 = 220 QUID - 99.022 = 220. ekar) 0.4501 = elk K = ln(6.4501) -0.072 [K= -0.072

(c) K= -0.072 Here ekt depends only on If "tes the ext If 't' is ove ekt So, the corred options sign of increases decreases are B E D I