Solve by Table/Function Regression

Percentage-Based Relationship on the SAT: Desmos Walkthrough

Apply each percent change to a starting value of 100 on one line, then subtract 100 to read the net percent change.

This lesson uses Desmos tables and regressions: drop the given values into a table, fit the model with a regression line, and read the constants straight off the fit.

Take this lesson interactively

A real SAT-style question

The value of a collectible comic book increased by $167 percent sign$ from the end of $2011$ to the end of $2012$ and then decreased by $16 percent sign$ from the end of $2012$ to the end of $2013$ . What was the net percentage increase in the value of the collectible comic book from the end of $2011$ to the end of $2013$ ?

$124.28 percent sign$

$140.28 percent sign$

$151.00 percent sign$

$209.72 percent sign$

How to solve it in Desmos, step by step

The idea

Let Desmos apply both percent changes to a starting value of 100, then read the net increase straight off one expression.

1
Step 1
Type this line. It starts the comic at value 100, grows it by 167 percent (multiply by 2.67), then shrinks that result by 16 percent (multiply by 0.84). Desmos shows the ending value, 224.28, on the right.
Type in Desmos
$v_{1}=100\cdot 2.67\cdot 0.84$
2
Step 2
Type this line to get the net percentage increase from the starting value. Desmos shows 124.28 on the right, which matches choice A.
Type in Desmos
$v_{1}-100$

The answer is A.

$124.28 percent sign$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

The value of a rare baseball card increased by

145

percent from the end of 2015 to the end of 2016 and then decreased by

22

percent from the end of 2016 to the end of 2017. What was the net percentage increase in the value of the rare baseball card from the end of 2015 to the end of 2017?

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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