Please help me out with my math homework, thank you!

Question

Oil flows into a tank according to the rate , and at the same time empties out at the rate , with both F(t) and E(t) measured in gallons per minute. How much oil, to the nearest gallon, is in the tank at time t = 12 minutes. Please show the setup

Answer 1

Hi, Madison:

Since the tank fills according to F(t) and empties according to E(t), the amount in the tank after time, t, is simply the difference of these 2 functions: F(t) - E(t) = (t²+1) / (t + 1) - ln (t + 7) / (t + 2).

Therefore, amount of oil in tank when t = 12, is (12² + 1) / (12 + 1) - ln (12 + 7) / (12 + 2)

= 145/13 - ln(19) /14

= 11.15 - .21

= 10.94 gallons

= 11 gallons, rounded to nearest gallon.