Exam 1: Functions and Change

A town has 1200 people initially. Find the formula for the population of the town, P, in terms of the number of years, t, if the town grows at an annual rate of 8% a year.

The following table gives values for three different functions. Find a formula for the exponential one.

Find a formula for the exponential function partially defined in the following table. Round any constants to 3 decimal places.

A bar of soap starts out weighing 125 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5 grams per day.

Give a possible formula for the function shown in the following table.

As , _____.

Identify the function defined in the following table as potentially linear, exponential, or neither.

A school library opened in 1980. In January of 2000, they had 16,000 books. One year later, they had 16,840 books. Assuming they acquire the same number of books at the start of each month, give a linear formula for the number of books, N, in the library as a function of the number of years, t, the library has been open.

The graph of is shown in the following figure. Is the graph increasing or decreasing at x = 3?

Simplify , leaving your answer as a fraction where appropriate.

As , the function _____.

If the size of a bacteria colony doubles in 6 hours, how many hours will it take for the number of bacteria to be 5 times the original amount? Round to 3 decimal places.

Using the table, find the value of a if f is linear.

Write the function in the form . Round a to 3 decimal places.

The following table gives the number of students taking an applied calculus course at a community college. A. Find the average rate of change in the number of students taking the course between 2000 and 2004 (in students per year). B. If the average rate of change continues at the same rate as between 2000 and 2004, in which year will the number of students taking the course first exceed 900?

A graph of is given in the following figure. A. What is (to the nearest whole number)? B. What is the range of the function?

Give a formula for the following sinusoidal function as a transformation of .

One of the following tables of data is linear and the other one is exponential. The formula for the linear one is . Find the values of a and b to two decimal places. A. a=______ B. b=_____

The following table gives the number of students taking an applied calculus course at a community college. Find the change in the number of students taking the course between 2001 and 2004.

A town has 2400 people initially. Find the formula for the population of the town, P, in terms of the number of years, t, if the town shrinks by 70 people a year.