SOLUTION: The pressure of the oil in reservoir tends to drop with time. By taking sample pressure readings for a particular oil reservoir, petroleum engineer have found that the change ....

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Question 1096536: The pressure of the oil in reservoir tends to drop with time. By taking sample pressure readings for a particular oil reservoir, petroleum engineer have found that the change .... is given by the function P(t)=t^3-18t^2+81t where t is time in years from the date of the first reading.
a) Find P(0), P(3), P(5), P(10)
b) Over what period is the change (drop) in pressure increasing? decreasing?
c) Graph P(t)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P%28t%29+=+t%5E3+-+18t%5E2+%2B+81t+
+P%280%29+=+0+
+P%283%29+=+3%5E3+-+18%2A3%5E2+%2B+81%2A3+
+P%283%29+=+9+-+162+%2B+243+
+P%283%29+=+90+
-------------------
+P%285%29+=+5%5E3v+-+18%5E5%5E2+%2B+81%5E5+
+P%2810%29+=+10%5E3+-+18%2A10%5E2+%2B+81%2A10+
-------------------------------------
Here's the graph:
+graph%28+400%2C400%2C+-20%2C20%2C-30%2C200%2C+x%5E3+-+18x%5E2+%2B+81x+%29+
The derivative ( is this a calculus problem? ) tells you when
the function is increasing or decreasing

The funtion +P%28t%29+ is decreasing between the roots of the quadratic.
( find the roots usinf quadratic fromula )