The average prescription prices P (in dollars) from 1997 through 2004

Question

can be approximated by the model P=0.1220t^2 + 1.529t + 18.72, 7 <= t <=14, where t represents the year, with t=7 corresponding to 1997.

a) determine algebraically when the average retail price was $40 and $50. 

b)Verify your answer to part a) by creating a table of values for the model.

c) According to the model. when will the average retail price reach $75

d) Do you believe the model could be used to predict the average retail price for years beyond 2004? Explain your reasoning.

 

Help me please, my test is coming soon and I don't really know how to use my knowledge for application in this theme.

Answer 1

Part a)

 

Set P=40 into the equation.

 

40 = 0.1220t² + 1.529t + 18.72

 

 

Subtract 40 on both sides of the equation.

 

0 = 0.1220t² + 1.529t - 21.28

 

 

Now we have a quadratic equation.  Use the quadratic formula to solve for t:

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 0.1220

b = 1.529

c = -21.28

 

Plug in these values into the formula to solve for t.  You will obtain two values because of the plus/minus sign.  Accept the positive value of t, since time is always positive.

 

 

Do the same for  P=50

 

 

Part b)

 

When you create a table of values, you are evaluating the function by plugging in the independent values.  Remember, you did this when you were first introduced to basic graphing.  If you plug in the solution to evaluate the function, you should get a number that is equal to or very close to 40 and 50.  This is also called a checking your work.

 

 

Part c)

 

Follow the same procedure as in part a.

 

 

Part d)

 

Yes you can.  t=14 represents the year 2004.  So  t>14  represents the time beyond 2004.