Oil leaks from a tank At hour t 0 there are 220 gallons of

Oil leaks from a tank. At hour t = 0 there are 220 gallons of oil in the tank. Each hour after that, 3% of the oil leaks out. What percent of the original 220 gallons has leaked out after 6 hours? % If Q(t) = Q_0e^kt is the quantity of oil remaining after t hours, find the value of k. k = What does k tell you about the leaking oil? Select all that apply if more than one statement is true It is the amount that the oil that leaks out each second. It tells by what percent of oil decays each hour. Because it is negative, we know the amount of oil in the tank is decreasing. Because it is less than one, we know the amount of oil in the tank is decreasing. It gives the continuous hourly rate at which oil is leaking. It tells what percent of oil remains after each hour. None of the above

Solution

220 gallons of oil

3% of oil leaks out every hour.

a) After 6 hrs remaini oil = (1- 0.03)^6(220) = 183.25 gallons

Amt of oil leaked = 220 - 183.25 = 36.75 gallons

b) Q(t) = Qoe^kt

= 220e^(kt) = 220(e^k)^t

= 220(0.97)^t

Comparing the two RHS equations : 0.97 = e^k ;ln0.97 = k

b) k = -0.03

c) Correct option C , E