Solve by Graphing

Exponential Increase Factor on the SAT: Desmos Walkthrough

Let Desmos turn a percent increase into a multiplier on one line: type

1+

the percent as a decimal and read the factor.

This lesson solves by graphing: turn the equation into curves, then read intersections, vertices, or tangency straight off the Desmos graph.

Take this lesson interactively

A real SAT-style question

The population of City A increased by $7 percent sign$ from $2015$ to $2016$ . If the $2016$ population is $k$ times the $2015$ population, what is the value of $k$ ?

$0.07$

$0.7$

$1.07$

$1.7$

How to solve it in Desmos, step by step

The idea

A 7 percent increase means multiplying by 1 plus 0.07. You can let Desmos do that addition for you and read the multiplier directly.

1
Step 1
Type this line. It tells Desmos that k is the starting amount (1) plus a 7 percent increase (0.07).
Type in Desmos
$k=1+0.07$
2
Step 2
Look at the value Desmos shows for k in that line. It reads 1.07, which is choice C.

The answer is C.

$1.07$

Now you try one

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

The population of City B increased by 4 percent from 2018 to 2019. If the 2019 population is

k

times the 2018 population, what is the value of

k

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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