SAT Math formula sheet · all 24 · Advanced Math · #11 of 24

Exponential growth and decay on the SAT: How It Is Tested

Nonlinear functions

Exponential Equation diagram for the SAT: Two things to know: the number in front is the initial value, and the number inside the parentheses, with the exponent,
What it is really testingTwo things to know: the number in front is the initial value, and the number inside the parentheses, with the exponent, represents the increase or decrease (usually in terms of percent).

The question from the sheet

Hard
SAT Advanced Mathanswer 12
For the function ff, f(0)=75f(0) = 75, and for each increase in xx by 11, the value of f(x)f(x) decreases by 60%. What is the value of f(2)f(2)?
Student-produced response: 12

How the diagram applies

  1. aa is the value at x=0x = 0: a=75a = 75. Decrease of 60%60\% means multiply by 1−0.60=0.401 - 0.60 = 0.40 each step.
  2. f(x)=75(0.4)xf(x) = 75(0.4)^{x}
  3. f(2)=75(0.4)2=75(0.16)=12f(2) = 75(0.4)^{2} = 75(0.16) = 12.

Answer: 12

That is 1 of 24.

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Common Questions

It comes up as an SAT nonlinear functions question. Two things to know: the number in front is the initial value, and the number inside the parentheses, with the exponent, represents the increase or decrease (usually in terms of percent).

a is the value at x = 0: a = 75. Decrease of 60\% means multiply by 1 - 0.60 = 0.40 each step. f(x) = 75(0.4)^x f(2) = 75(0.4)^2 = 75(0.16) = 12.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Exponential Equation is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.