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Exponential Functions and Halving Time
Write the given rate as a decimal. This is $\displaystyle {b}$ (DECAY FACTOR). Solve by graphing and INTERSECTION method Set up the equation $\displaystyle {a}{b}^{{t}}={0.5}{a}$ Determine initial value of the model (i.e. initial population, initial investment, initial salary, etc.). Set up the equation $\displaystyle {a}{b}^{{t}}={2}{a}$ Write the model using appropriate function notation (i.e. $\displaystyle {P}{\left({t}\right)}={a}{b}^{{t}}$ , $\displaystyle {V}{\left({t}\right)}={a}{b}^{{t}}$ , $\displaystyle {S}{\left({t}\right)}={a}{b}^{{t}}$ , etc.)

Exponential Functions and Halving Time

Which of the following steps can be used to help write an Exponential Decay Model and to use that model to determine the Halving Time of the Function? Check all that apply.

Write the given rate as a decimal. This is $\displaystyle {b}$ (DECAY FACTOR).
Solve by graphing and INTERSECTION method
Set up the equation $\displaystyle {a}{b}^{{t}}={0.5}{a}$
Determine initial value of the model (i.e. initial population, initial investment, initial salary, etc.).
Set up the equation $\displaystyle {a}{b}^{{t}}={2}{a}$
Write the model using appropriate function notation (i.e. $\displaystyle {P}{\left({t}\right)}={a}{b}^{{t}}$ , $\displaystyle {V}{\left({t}\right)}={a}{b}^{{t}}$ , $\displaystyle {S}{\left({t}\right)}={a}{b}^{{t}}$ , etc.)

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