Question

exponential fun graphic organ y = 4(\frac{2}{3})^x a = \underline{\quad\quad\quad\quad\quad\quad} b = \underline{\quad\quad\quad\quad\quad\quad} growth or decay?

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( y = a(b)^x \), where \( a \) is the initial value and \( b \) is the base.

Step2: Identify \( a \) in \( y = 4(\frac{2}{3})^x \)

Comparing with \( y = a(b)^x \), we see that \( a = 4 \).

Step3: Identify \( b \) in \( y = 4(\frac{2}{3})^x \)

Comparing with \( y = a(b)^x \), we see that \( b=\frac{2}{3} \).

Step4: Determine Growth or Decay

For an exponential function \( y = a(b)^x \), if \( 0 < b < 1 \), it is a decay function. Since \( 0<\frac{2}{3}<1 \), it is a decay function.

Answer:

\( a = 4 \)
\( b=\frac{2}{3} \)
Growth or Decay? Decay