M120 Project on Integration Concepts

Date Due: Value:  25 points

                                                                                                5 pt penalty for each class day late

For 1 & 2, find two functions that have the given derivative, and sketch the graph of each.  (There is more than one correct answer.)

1.                                                                     2.

For 3 & 4, find the equation of the particular solution that passes through the indicated point.

3.                                                            4. 

For 5 & 6, find a Function f  that satisfies the given conditions. 

5.              6. 

For 7 – 10, solve the application problems.

7.  The marginal cost of a product is modeled by   when x = 13, C = 100

     Find the cost function.

8.   A population of bacteria is growing at the rate of   where t is the time in days. 

      When t = 0, the population is 1000.

a)  Write an equation that models the population P in terms of the time t.

            b)  What is the population after 3 days?

            c)  After how many days will the population be 12,000?

9.  The marginal price for the demand of a product can be modeled by  where x is the

     quantity demanded.  When the demand is 600 units, the price is $30.

     a)  Find the demand function, p = f(x).

     b)  Use your calculator to graph the demand function.  Does the price increase or decrease as the

            demand increases?

     c)  Use the zoom and trace features of your calculator to find the quantity demanded when the

            price is $22.

10.  From 1986 through 1992, the number of automatic teller machine (ATM) transactions T (in millions)

      in the  United States changed at the rate of   where t = 0

      corresponds to 1986.  In 1992, there were 600 million transactions per year.

            a)  Write a model that gives the total number of ATM transactions per year.

            b)  Use the model to find the number of ATM transactions in 1986.