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Solve by Table/Function Regression

Yearly Decay Rate on the SAT: Desmos Walkthrough

Graph the value function and let Desmos compute how much is lost over one full year, 100(1−f(12)/f(0))100(1-f(12)/f(0)), to read the percent decrease.

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

f(x)=5,470(0.64)x12

The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of its value the preceding year, what is the value of p ?

A

4

B

5

C

36

D

64

How to solve it in Desmos, step by step

The idea

Graph the value function, then have Desmos compute how much value is lost over one full year (12 months). That loss percent is exactly p.

  1. 1

    Step 1

    Type this function. Desmos draws the value curve over x months.

    Type in Desmos

    f(x)=5470(0.64)x12f\left(x\right)=5470\left(0.64\right)^{\frac{x}{12}}
  2. 2

    Step 2

    Type this to get the fraction of value still left after one full year (12 months). Desmos shows the result equals 0.64.

    Type in Desmos

    f(12)f(0)\frac{f\left(12\right)}{f\left(0\right)}
  3. 3

    Step 3

    Type this to turn that into the percent lost each year. Desmos shows the result equals 36.

    Type in Desmos

    100(1−f(12)f(0))100\left(1-\frac{f\left(12\right)}{f\left(0\right)}\right)
  4. 4

    Step 4

    Read the displayed value, 36. The equipment loses 36 percent of its value each year, so p equals 36, which is choice C.

The answer is C.

36

Now you try one

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

f(x)=7,310(0.72)x/12f(x) = 7{,}310(0.72)^{x/12} The function ff gives the value, in dollars, of a certain piece of equipment after xx months of use. If the value of the equipment decreases each year by pp percent of its value the preceding year, what is the value of pp?

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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