Exam 3: Linear Equations With Two Variables

In 1990 a town s population was 24127. In 1998 the town s population increased to 33887. Assuming that the population increased exponentially from 1990-1998 this data can be modeled by where t is the number of years since 1990.

Use the graph to find the x- intercept.

The number of tourists in a small town at time t (in years) is modeled by . What is the decay rate (in percentage form)?

Find the slope of the equation .

The population of Smallville at time t (in years) is modeled by . What is the growth factor?

Find the slope of the equation .

Determine whether the following relation is a function. For the year 2009 the input is the day of the year (1 to 365) and the output is the temperature at noon in degrees Fahrenheit.

Graph the equation using the slope and y- intercept. Graph at least three points. Clearly label and scale the axes.

Determine the equation of the line that passes through the given points. Put the final answer in form. Points:

The graph of every equation is a line.

Evaluate the function. ; find .

The population of Smallville at time t (in years) is modeled by . What is the initial population of Smallville?

The cost for a birthday party at Party Tymes is $50 plus $15 for each child. The cost equation is where C is cost in dollars for k children. The limit at Party Tymes is 18 children. Graph this equation.

The graph displays the number of tickets available (not yet sold) for the number of hours since the theater opened at noon. Calculate the slope for the Shoot-em Up line and interpret its meaning.

After college graduation Sheena was offered two different jobs. The first offer included a salary of $41200 plus a guaranteed raise of $1100 per year. The second offer included a salary of $32900 plus a guaranteed raise of 3% per year. Use the second job offer to find a function g that models the salary t years from now.

Using the following table of a function that models exponential growth determine the initial value of the population (rounded to the nearest integer).

Rewrite the linear equation in general form.

Morphine is administered to a patient intravenously with an initial amount of 11 mg. About 36.9% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body after t hours?

is a function that represents the cost in dollars to make w widgets. Find .

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. True or false? The population of f(t) after 4 years exceeds the carrying capacity for the logistic function.