ALG1.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.

Algebra I · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
exponential functionsformf(x) = abxbrational numbermathematical situationsreal-world situationsgrowthdecay
Skills
  • write (exponential functions in the form f(x) = abx) #dok2
  • describe (mathematical situations using exponential functions) #dok2
  • describe (real-world situations using exponential functions) #dok2
  • interpret (parameters a and b for growth and decay) #dok2
Learning Targets
  • I can write exponential functions in the form f(x) = abx where b is a rational number. #dok2
  • I can describe mathematical and real-world situations, including those involving growth and decay, using exponential functions. #dok2
  • I can recognize when an exponential function is appropriate to model a situation involving growth or decay. #dok2
  • I can identify and interpret the values of a and b in an exponential function in context. #dok2
  • I can construct an exponential function from given information about a growth or decay situation. #dok3
Big Ideas
  • Exponential functions can be used to model a variety of mathematical and real-world phenomena, especially those involving repeated multiplication such as growth and decay.
  • The parameters in exponential functions, specifically a and b in f(x) = abx, determine the initial value and the rate/nature of change in the modeled situation.
Essential Questions
  • How can we use exponential functions to represent real-world growth and decay situations?
  • What do the parameters a and b represent in the equation f(x) = abx?
  • How do we decide whether a situation should be modeled using an exponential function?
  • What is the effect of changing a or b in an exponential function on the model or situation?
  • How can exponential functions help us make predictions about future or past events?