Skip to main content

Quantitative Skills and Reasoning Activity Workbook

Megan Patnott

Section 9.1 Applications of Exponential Models Prep Activities

Prep Activity 9.1.1.

Consider an item initially priced at $549.9, but which has had its price reduced by 10% several times in a row.
🔗

(b)

Find a formula for the item’s new price after \(n\) markdowns.
🔗
🔗

(c)

Use your formula to find the item’s new price after 3 markdowns.
🔗
🔗

(d)

How many markdowns will it take for the item’s price to be $300 or less? How do you know?
🔗
🔗
🔗

Prep Activity 9.1.2.

Cars lose value over time. This is called depreciation. Let’s use information from carfax.com
 1 
www.carfax.com/blog/car-depreciation
to analyze the change in the value of a brand new Subaru Crosstrek over time. Suppose the Crosstrek was purchased for $26,796.
🔗

(a)

The Carfax article says that the value of a new vehicle can drop by 20% after 1 year. Find the change factor, and use the change factor to estimate the value of Crosstrek in a year.
🔗
🔗

(b)

The Carfax article says that after the next four years, you can expect a car to lose about 15% of its value each year.
🔗
(ii)
Estimate the value of the Crosstrek after 2, 3, 4, and 5 years using the change factors. Don’t forget that the change factor is different for the 1st year!
🔗
🔗
(iii)
Suppose that the car’s value continues to depreciate at 15% per year. Find a formula for the value of the Crosstrek after \(t\) years.
🔗
🔗
🔗

(c)

The Carfax article also says that 20% depreciation in the first year, followed by 15% depreciation for the next four years, is about the same as saying that a car is worth 40% of its purchase price after five years.
🔗
(i)
Is 40% the change factor or the percent change? Explain how you know.
🔗
🔗
(ii)
If 40% is the change factor, find the percent change. If 40% is the pecent change, find the change factor.
🔗
🔗
(iii)
Use the change factor to estimate the value of the Crosstrek after 5 years. How similar is your answer to your previous estimate?
🔗
🔗
🔗
🔗

Prep Activity 9.1.3.

You’ll need to be able to do the following things for this lesson. Rate how confident you are on a scale of 1 - 5 (1 = not confident and 5 = very confident).
🔗
Table 9.1.1.
🔗
Skill or Concept: I can … Rating from 1 to 5
Set up and evaluate exponential models given starting values and percent change.
🔗
🔗
PrevTopNext