Crude oil is leaking from a tank at the rate of 10% of the tank volume every 3 hrs. If the tanker originally contained 500,000 gallons of oil, how many gallons of oil remain in the tank after 4 hrs? Round to the nearest gallon.

  434,470 gallons

Step-by-step explanation:

The exponential equation for the volume v remaining after t hours can be written as ...

  v(t) = (initial amount)×(decay factor)^(t/(decay time))

  v(t) = 500,000×(1 -10%)^(t/3)

Then after 4 hours, the remaining volume is ...

  v(4) = 500,000×(0.90^(4/3)) ≈ 434,470 . . . . gallons

Comment on the form of the equation

The decay factor is related to the decay rate by ...

  decay factor = 1 - (decay rate)

and the decay time is the time applicable to that decay rate. Here, the rate is 10% every 3 hours, so the decay time is 3 hours for a decay rate of 10%.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!