Chapter 7

Students who fill in an exponent of 6 or 7 for y in the second equation, may not understand the effect of y^ -1 in the denominator. Remember that y ^-1 in the denominator is the same as y^1 in the numerator.

Students who simplify the second expression incorrectly, may benefit from breaking the problem down into smaller steps. Suggest you look at the negative exponents first. Next, look at the exponents outside of the parentheses, and then combine like terms.

What are the third and fourth terms of the sequence?

Suggest that students use a process of elimination. First, think about the effect of b on the graph of an exponential function. If b > 1, then the absolute value of y increases as x

increases, which is what the graph shows. Based on this, can eliminate the second and fourth choices. Next, think about the effect of a. Since b is positive, if a is also positive, then value of the function will always be positive. The graph shows that the value of the function is always negative, so a must also be negative. Therefore, the third

choice is correct.

Students may use 500 in their formulas. Remember that 500 feet is the height of bounce 0. In other words, a recursive formula of

a 0 = 500, a n = 0.8( an - 1 ) is an acceptable alternative, as long as the subscript for the initial value is 0, not 1. This formula still gives a height of 400 feet for bounce 1 and a height of 320 feet for bounce 2.

Students may not understand how to use the ordered pairs to find the equation.Remember you can use the ordered pairs to set up two equations with two unknowns, a and b. Solve one equation for a, then use substitution

to solve the other equation for b.

The 2010 model of a certain type of car travels 32 miles on a gallon of gas. The manufacturer increased that car’s gas mileage by 6% each model year. On a 1000 mile trip, how many fewer gallons of gas, to the nearest tenth of a gallon, does a 2015 model use than a 2011 model? Show your work.

This gives lots of information but asks one very specific question. Students should outline the steps they will take to find the answer before they begin. This will help them to stay focused on working toward the answer to the question that is asked.