Exponential Functions Target 3A

EX.1 Growth Factor TEACHER : Markups, Discounts & Taxes

• multiply by a number greater than 1, the quantity is increased
• multiply by a number less than 1, the quantity is decreased
• multiply by 1, the quantity is unchanged.

Launch:

A woman’s bag originally priced at $25.00 is advertised at 20% off during a clearance sale. What is the selling price of the bag?

Students need to recall that 20% = 0.2.

We anticipate students will multiply $25 by 20% and then add to $25.

By the end we expect students to multiply by the growth rate 1.25.

What to bring out in the DEBRIEF:

• The growth rate is the percent increase or decrease.
• The growth factor is 1 + percent increase or 1 – percent decrease.
• To find the changed quantity, multiply original quantity by the growth rate.

Assessment:

On the launch, find out if students are using proportional thinking. By the end of the lesson, we want them to use an expression.

#6 Can they write an expression for the launch problem?

#7 & 8 Find a discount price and a markup price.

#17 – 18 Find percent increase, percent decrease or determine the price is unchanged.

#21 – 22 Problems work backward.

#24Find price after discount and salestax added.

Common Core Standards

Exponential Functions Learning Targets

Practice 2 Reason abstractly and quantitatively.

Practice 4. Model with mathematics.

Practice 6 Attend to precision.

A-SSE.1aInterpret expressions that represent a quantity in terms of its context.
a Interpret parts of an expression, such as terms, factors, and coefficients.

• Identify the initial value and growth rate of exponential expressions.

F.BF.1 a Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.1 b Write a function that describes a relationship between two quantities.
b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

• Write a function that models a exponential relationship.

Big Idea A: Students will find and interpret key features of exponential relationships (growth rate, intervals where the function is increasing or decreasing, intercepts, domain/range, inputs and outputs, asymptotes) from multiple representations in context.

Launch:

A woman’s bag originally priced at $25.00 is advertised at 20% off during a clearance sale. What is the selling price of the bag?

Students need to recall that 20% = 0.2.

We anticipate students will multiply $25 by 20% and then add to $25.

By the end we expect students to multiply by the growth rate 1.25.

1. Complete the multiplication table.

1. Compare the values you wrote in the table in Row 2 with the given values in the Row 1 by subtracting Row 2 – Row 1.

1. Compare the values you wrote in the table in Row 2 with the given values in the Row 1 by subtracting Row 3 – Row 1.

The following definitions are from google.com

Remember, the column headings of the first table are in dollars.

1. In which row are we finding a markup?

Row 3 because the prices increase.

1. In which row are we finding a discount?

Row 3 because the prices decrease.

1. Receiving a 20% discount is the same as paying _80_ % of the original price.

1. Use your answer from the Launch, and the information in the “25” column to use one expression to find the answer to the launch.

Write the expression: _25 × 0.8______

Launch:

A woman’s bag originally priced at $25.00 is advertised at 20% off during a clearance sale. What is the selling price of the bag?

Write one expression to find the new price.

1. a) In the launch we found the sale price was $20.

• Write an expression to find the total cost to buy the bag including 8% sales tax.
• Find the new cost including sales tax.

25 X 1.08

$27

Clark County, Washington actually charges 8.24% sales tax.

• Write an expression to find the total cost to buy the bag including 8.24% sales tax.
• Find the new cost including sales tax.

25 X 1.0824

$27.06

1. Suppose the next day, the sale is now 30% off of the original price.

• Write an expression to find the total cost of buy the bag including Clark County sales tax.
• Find the new cost including sales tax.

25 X 0.7

$17.50

Solve.

1. A pair of jeans originally priced at $30.00 is advertised at 25% off during a clearance sale. What is the selling price of the jeans?

30 X 0.75 = $22.50

1. A computer software retailer used a markup rate of 30%. Find the marked up price of a computer game that cost the retailer $15.

15 X 1.30 = $10.50

Greater, Less or Equal?

When the initial value on the left is multiplied by the growth factor on the right, is the product greater, less or equal? Write the growth rate in the corresponding column.

The growth factorin the previous table is used to determine percent increases or percent decreases. Determine the growth rate and whether it is an increase, decrease or unchanged.

For problems #23 – 27

• Show the steps you used to solve the problem.
• Include an answer with units.

Finding the Discount and the Selling Price.

1. The marked price of a branded flat 32’ LCD television is $300. It was offered during a sale at 10.5% discount. What was the discount? What was the selling price?

Finding the Markup

1. An item bought for $1,200 is sold for $1,500. What is the markup rate?

1. An appliance store uses a 30% markup on cost. Find the cost of dishwasher that sells for $520.

Finding Tax

1. A family had dinner in a restaurant and paid $64 for food. They also had to pay 12.5% sale tax and 15% for the tip. How much did they pay for the dinner?

1. Suppose Jane purchased a pair of shoes that was priced at $44.25, yet the total bill was $47.79. What is the sales tax rate in this city?

Mini-Lessons

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