oil leaks from a tank. At t=0 there are 250 gallons of oil in the tank. Each hour after that 4% of the oil leaks out

Question

a. What percent of the original 250 gallons has leaked out after 10 hours?

250e^.04(10)=372.96--> 3.73% is what I got my professor said its correct

b. If Q(t)=Qoe^kt is the quantity of oil remaining after t hours, find the value of k. What does k tell you about the leaking oil?

Answer 1

By doing this problem 1 hr at a time: 1hr=250*.96=240

2 =230.4

3 =221.18

4 =212.34

5 =203.84

6 =195.69

7 =187.86

8 =180.35

9 =173.13

10 =166.21

so166.21/250=66.48% was lost.

The way it's written; each hr 96% of each level is left.

Each amount is "k" for that hr.

Answer 2

250e^(.04t) = Qoe^(kt). Now Qo represents the initial amount which is 250.

250e^(.04t) = 250e^(kt)

e^(.04t) = e^(kt)

(.04t) = (kt)

.04 = k

What does k tell you? Since k=.04 what do you think k represents? Hint: where did .04 come from?