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Test: Exponential equations and models

This test covers exponential equations and their use in growth and decay models. Students rewrite expressions with a common base, solve equations and interpret percentage, compound and periodic change.

Question qty: 10
Duration in minutes: 18
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Sample questions

  • When does y = a^x increase or decrease?
  • Compare y = a^x and y = b^x when 1 < a < b and x > 0.
  • Solve a^(x + b) = a^c.
  • What multiplier represents a p% increase per period?
  • Solve a^x = v.
  • Initial value s decreases by p% yearly. Find it after n years.
  • Initial value s grows by p% yearly. Find it after n years.

Exponential equations and models

In an exponential equation, the unknown appears in an exponent. If both sides can be written with the same positive base other than one, equate the exponents. Otherwise apply logarithms.

Growth and decay

The model y = abˣ represents growth for b > 1 and decay for 0 < b < 1. A percentage change p corresponds to multiplier 1 + p or 1 − p when p is a decimal. Identify the initial value, time unit and whether change compounds repeatedly.

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