2.4.1: Preparation M.4

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(1) Zeke is driving from his house to the beach and wants to model how far he is from home. He is currently 50 miles from home and will drive 65 mph until he reaches the beach. Which of the following equations models this situation? Let t be time in hours and D be distance in miles from Zeke’s home.

(i) D = 50 – 65t

(ii) D = 50 + 65t

(iii) D = 65 + 50t

(iv) D = 65 – 50t

(2) Ezra has a base salary of $25,000 and earns 65% commission on vacuum cleaners. This means that for each vacuum cleaner he sells, he earns an additional amount that equals 65% of the price of the vacuum cleaner. To answer the following questions, use a model where S is Ezra’s total salary and v is the total dollar amount of his vacuum cleaner sales.

(a) What is the dollar amount of sales in vacuum cleaners Ezra will need to make in a year if he wants to earn $35,000? Round to the nearest cent.

(b) If vacuums are sold for $200 each, how many vacuum cleaners would Ezra need to sell in a year to make $35,000? Round to the nearest whole number of vacuum cleaners.

(3) The number of members in a professional organization increased each year for ten years, starting in 2013. The result can be modeled by the equation M = 1,200 + 250t.

(a) What do you think the variables M and t represent?

(b) What was the rate of the organization’s growth? How large was the organization’s membership at the start of the growth period? Explain what your answers mean in the context of the question.

After Preparation M.4 (survey)

You should be able to do the following things for the next collaboration. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Collaboration M.4, you should understand the concepts and demonstrate the skills listed below:

Skill or Concept: I can …	Rating from 1 to 5
recognize when a linear model is appropriate.
write an algebraic equation for a line given the y-intercept and slope.
solve a linear equation.

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