Question

PART B The percentage of American adults with an annual income of thousand dollars who watch cable television can be modeled by the function p = f(1) = 4.71V1 + 45.37. 1) Sketch a graph of this function on the given grid. Draw a set of axes, label your axes with words and numerical scales. (6 points) 2) Is this function increasing or decreasing? (1 point) 3) What is the domain of this function? (use interval notation!) (2 points) 4) What is the range of this function? (use interval notation!) (2 points) 5) Find the p-intercept. What does it mean in this situation? (2 points) 6) Estimate the percentage of adults with an annual income of $40,000 who watch cable television. Show how you use the equation to find this. (2 points)

Answer 1

Here the function p is diffrentiable. So it is continues. Let us draw it on a white paper.
1)
2) Inspecting the graph, we have the fact that p is increasing from point to point. Note that the function pocess a positive slope at any point.

3) The function takes a positive value for the income ( None of us a have negative income) and it could be zero. Again we can not properly find an upper limit of someone's income. So we have to analyse this function upto infinity.
Hence the domain is [0,∞)

4) By the defenition of the function, the least possible value of acceptance is 45.37. Let x be a number grater than 45.37. Set x=p=4.71$\sqrt{I}$+45.37
Then 4.71$\sqrt{I}$=x-45.37
That is, $\sqrt{I}$ =(x-45.37 )/4.71, positive. Then I is the positive squareroot of this positive value.

That is p takes all the values grater than 45.37. Hence the range is [45.37,100]

5) In this case the p-intercept is 45.37 at I=0 ( Found from inspecting the graph). In this scenario, it means that, 45.37% of people watch cable television even if they have no income.