Question

Oil leaks from a tank. At hour t = 0 there are 240 gallons of oil in the tank. Each hour after that, 7% of the oil leaks out. (a) What percent of the original 240 gallons has leaked out after 11 hours? % (b) If Q(t) = Q_0e^kt 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 what percent of oil remains after each hour. B. It tells by what percent of oil decays each hour. C. Because it is negative, we know the amount of oil in the tank is decreasing. D. It gives the continuous hourly rate at which oil is leaking. E. Because it is less than one, we know the amount of oil in the tank is decreasing. F. It is the amount that the oil that leaks out each second. G. None of the above

Answer 1

Let Q(t)-ab' be denote the number of gallons left in the tank after t hours strarting amount is a -240 The percent left in the tank after 1 hour, is 93% So, e()240 (0.93 After 11 hours 2(11) 240 (0.93)108.024gallons left in the tank 108.024 0.45-45%of what had initially been in the tank. 240 Therefore, about 55% leaked out 0.55-elk İlk ln(0.55) kIn (0.55) c) The corect choice C 0.05