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.)
For 3 & 4, find the equation of the particular solution that passes through the indicated point.
For 5 & 6, find a Function f that satisfies the given conditions.
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
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.