Question

The Global spending on travel and tourism (in billions of dollars) is given by the eq. y=1.69x^2-.92x+324.10, where x equals the years after 1990.

a.) Using graphical methods (the intersection method) find the year in which spending is projected to reach 1817.5 billion. Write down the vertex and window you set. "Sketch" whats on the screen for the graph and give a solution.

b.) Repeat the same problem but solve it using the quadratic formula.

c.) The profit function is given by P(x)=-2x^2+220x-2000 where x is the number of home theatre systems produced and sold. P(x) is measured in dollars. Using the graphing calculator, find the x-intercepts which would be the number of units produced and sold to break even. Write down window setting and show steps.

Answer 1

y=1.69x^2-.92x+324.10

Plot the graph for above function

Then plot y = 1817.5 billion on the same graph and check the point of intersection.

Vertex : (0, 324.1)

point of intersetion : ( 30,1817.5)

Scale of graph :

b) Using Quadratic formula :

y=1.69x^2-.92x+324.10 and  y = 1817.5

So,1.69x^2 - 92x + 324.10 = 1817.5

1.69x^2 - 92x - 1493.4 =0

Solve the equation :

Now after solving values of x:

x = 30 , and x = -29.45

Neglect -ve value So, we have same value of x = 30 as from graohical solution

c) PLot the graph for profit function

P(x)=-2x^2+220x-2000

Breakeven point is when P(x) =0

So, look for x intercept from graph

So, from the graph we can see that there are tow values of x ith breakeven:

x = 10 and x = 100