Assignment:
Part I: Modeling
Your mission is to find real-world data for company sales, a stock price, biological growth, or some sociological trend over a period of years that fits an exponential, logistic, or logarithmic function. To do this, you can look at a statistical graph called a histogram which describes the situation or at a graph or table describing it. Once you have found data consisting of numerical values, you are to find the equation that is the best exponential, logistic, or logarithmic fit for the data and then write the model that describes the relationship. Some helpful steps for this process:
Q1. If you have a table of values for different years, create a graph of the data to determine the type of function that will be the best fit for the data. To do this, first align the independent variable by letting the input represent the number of years from some convenient year and then enter the data into your graphing technology and draw a scatter plot. Check to see if the points on the scatter plot lie near some curve that could be described by an exponential, logistic, or logarithmic function. If not, save the data for possible later use and renew your search. You can also test to see if the percent change of the outputs is nearly constant for equally spaced inputs. If so, the data can be modeled by an exponential function.
Part II : Printing
A printer has a contract to print 100,000 invitations for a political candidate. He can run the invitations by using any number of metal printing plates from 1 to 20 on his press. Foe example, if he prepares 10 plates, each impression of his press makes 10 invitations. Preparing each plate costs $8 and he can make 1000 impressions per plate per hour. If costs $128 per hour to run the press, how many metal printing plates should the printer use to minimize the cost of printing the 100,000 invitations.
Q1. Write a function of x that gives the total cost of producing the invitations.
Provide complete and step by step solution for the question and show calculations and use formulas.