8adv.MATH.9.C

Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay.

Grade 8 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
exponential functionsformf(x) = ab^xrational numberproblemsmathematical situationsreal-world situationsgrowthdecay
Skills
  • write (exponential functions in the form f(x) = ab^x where b is a rational number) #dok2
  • describe (problems arising from mathematical and real-world situations using exponential functions) #dok3
  • identify (growth and decay situations that can be modeled by exponential functions) #dok2
  • interpret (the meaning of a and b in real-world contexts) #dok2
Learning Targets
  • I can write exponential functions in the form f(x) = ab^x with a rational base. #dok2
  • I can identify whether a real-world or mathematical situation represents exponential growth or decay. #dok2
  • I can describe how to model a real-world problem involving repeated multiplication with an exponential function. #dok3
  • I can explain the process for selecting rational values for b to fit a given scenario. #dok3
  • I can interpret the meaning of the a and b values in an exponential function in context. #dok2
Big Ideas
  • Exponential functions can model real-world and mathematical situations that involve repeated multiplication, such as growth and decay.
  • Writing exponential functions with rational bases allows for accurate representation and prediction of growth or decay in various contexts.
Essential Questions
  • How do you recognize when a situation can be modeled by an exponential function?
  • What information do you need to write an exponential function for a real-world problem?
  • How does the value of b affect whether an exponential function models growth or decay?
  • Why is it important to use a rational number for the base b in exponential functions?
  • How can you use an exponential function to make predictions in mathematical and real-world contexts?