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How to Solve SAT Exponential Growth Questions with Desmos

Last updated: October 12, 2026

Type the growth model on one row of Desmos and the target value on the next, then click where the curve crosses the line. The x-coordinate of that crossing is the answer. You skip the logarithms and you don't need to guess and check powers.

The problem

Solve: 5(2ˣ) = 40
Solution: x = 3

Read it as a quantity that starts at 5 and doubles every step. The question asks how many steps it takes to reach 40.

What do you type?

Two rows:

Row 1: y = 5*2^x
Row 2: y = 40

Desmos turns the asterisk into a dot, so Row 1 reads y = 5·2ˣ. Row 1 is the curve and Row 2 is the target, a flat line.

Watch the exponent as you type. When you press ^, the cursor jumps up into the exponent and stays there. Anything you type next goes into the exponent until you press the right arrow key. Type 2^x+1 without the arrow and you get 2 to the power x + 1, which is a different curve that crosses the line in a different place. If the exponent is raised over anything more than the x, delete it and retype.

Why is the crossing off the screen?

The default window shows small numbers, and 40 sits a long way above them. All you see is the curve climbing off the top edge of the screen and no line at all.

Zoom out with the minus button in the corner of the graph, or scroll. Exponential curves stay close to the x-axis on the left and climb steeply on the right, so the crossing is always on the right side. Keep zooming until the flat line and the curve meet in view.

How do you read the answer?

Click the point where the curve meets the line. Desmos marks it with a gray dot and a label: (3, 40). The x-coordinate, 3, is the number of steps. The y-coordinate is the 40 you typed, which tells you that you clicked the right point.

There's only one dot, and that's the whole answer. A growth curve only goes up, so it can cross a flat line once at most. You don't need to check the left side for a second answer like you would with a parabola.

What if the question asks for the amount, not the time?

The same model can be asked backwards: what is the value after 3 steps? Keep Row 1 and type the step count as a vertical line:

Row 2: x = 3

Click where it meets the curve and the label reads (3, 40). This time the y-coordinate is the answer.

What if the question is written in percentages?

You still type a starting value times a growth factor raised to x. The difference is that the question gives you a percentage instead of the factor. Type the factor, not the percentage: 4% growth is 1.04 and 3% decay is 0.97. If you type 4 or 0.04 instead, the curve is wrong and Desmos still gives you a crossing.

There's a quick check. A growth curve rises from left to right and a decay curve falls. If the question says "decreases" and your curve climbs, fix Row 1 before you click anything.

Turning the scenario's words into the starting value and factor is covered in SAT Nonlinear Functions. This post only shows how to type and read the model once you have it.

What if the variable isn't x?

Word problems tend to use t for time or n for steps. Change it to x on every row before typing. Desmos treats any other letter as a constant and offers you a slider, so the curve never appears.

How do you practice this?

Pick 10 exponential questions from practice tests. For each one:

1. Write the model by hand first: the starting value, then the growth factor
2. Type the model and the target on two rows, zoom out until they meet, and click the crossing
3. When Desmos disagrees with your hand answer, check the exponent first, then check the growth factor, because those are the two places the typing usually goes wrong

The goal is a model you can build in 30 seconds and a crossing you can read in 10.

HIROSCORE tracks nonlinear functions as their own skill inside Advanced Math, so a habit of building the wrong growth factor shows up in your results instead of hiding in your overall math score. The GPS for your SAT score.