Exam 1: Functions and Change

Find the equation of the line passing through the points (0, -4) and (7, -3). Then determine if the line is increasing or decreasing.

You win the lottery and are offered a choice of $90,000 now or $20,000 at the end of each year for five years. Assuming a 5% annual interest rate and ignoring taxes, which is the better option?

Could the following table represent a linear function? Answer yes or no.

Suppose that is the distance in miles traveled in t hours by a car moving at 70 miles per hour. Give a formula for the function .

A quantity growing exponentially according to the formula has a doubling time of .

In the book One Grain of Rice, a girl receives a reward that starts with one grain of rice on day one, two grains on day two, four on day three and eight on day four. Each day, she receives double the number of grains of rice. How many grains of rice does she receive on the 20th day?

Consider the following graph. Between point A and point B, the graph is: (mark all that apply)

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Write a formula for the size of the image, N, after the original image of size a has been reduced n times with the copy machine set on 90% reduction.

As , _____.

Simplify the expression as much as possible.

If the graph of shrinks vertically by a factor of 1/2, then shifts vertically by 6 units, then stretches vertically by a factor of 3, the resulting graph is the same as the original graph.

Which could be a possible formula for the following figure? Assume a and b are positive constants.

The following table gives the values for . It is possible that y could be inversely proportional to x.

Production costs for manufacturing T-shirts consist of a fixed cost of $18,000 plus variable costs of $4 per shirt. Each T-shirt sells for $12 dollars. What is the marginal cost?

The graph of is shown in the following figure. The ________ of is , and the ________ of is .

A car is worth $15,000 when it is 1 year old, and it is worth $8,000 when it is three years old. A. Write the value of the car, V (in dollars), as a function of the age of the car, a (in years). Assume this is a linear function. B. How much does the car depreciate in value each year? C. How much was the car worth when it was first purchased?

Given the equation , find and simplify .

Which could be a possible formula for the following figure? Assume a and b are positive constants.

The average weight in pounds of American men in their sixties (in 1979) as a function of their heights in inches is given in the following table. The formula that expresses the weight w in terms of the height h is given by w = _____+_____h

Find a formula for the linear function f. .