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Unit 7 Target 3 Writing Exponential E Algebra 1
Write the equation for the exponential
1.





x

y


-2
-18


-1
-6


0
-2


1

-2//3








y= 
qquad

y=

Unit 77 Target 33 Writing Exponential E Algebra 11\newlineWrite the equation for the exponential\newline11.\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline2-2 & 18-18 \\\newline\hline1-1 & 6-6 \\\newline\hline 00 & 2-2 \\\newline\hline 11 & 2/3 -2 / 3 \\\newline\hline\newline\end{tabular}\newline22.\newliney= y= \qquad \newliney= \mathbf{y}= \newline44.\newline55.

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Q. Unit 77 Target 33 Writing Exponential E Algebra 11\newlineWrite the equation for the exponential\newline11.\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline2-2 & 18-18 \\\newline\hline1-1 & 6-6 \\\newline\hline 00 & 2-2 \\\newline\hline 11 & 2/3 -2 / 3 \\\newline\hline\newline\end{tabular}\newline22.\newliney= y= \qquad \newliney= \mathbf{y}= \newline44.\newline55.
  1. Identify Pattern in yy-values: Identify the pattern in the yy-values to determine the base of the exponential function.\newliney=abxy = a \cdot b^x\newlineWe see that when xx increases by 11, yy is multiplied by a constant factor.
  2. Find Constant Factor: Find the constant factor by dividing a y-value by the previous y-value.\newline(6)/(18)=13(-6) / (-18) = \frac{1}{3}\newline(2)/(6)=13(-2) / (-6) = \frac{1}{3}\newline(23)/(2)=13(-\frac{2}{3}) / (-2) = \frac{1}{3}\newlineThe constant factor is 13\frac{1}{3}, so b=13b = \frac{1}{3}.
  3. Determine Initial Value: Use one of the points to find the initial value aa. Let's use the point (0,2)(0, -2). 2=a×(13)0-2 = a \times (\frac{1}{3})^0 2=a×1-2 = a \times 1 So, a=2a = -2.
  4. Write Final Exponential Equation: Write the final exponential equation using the values of aa and bb.y=2×(13)xy = -2 \times \left(\frac{1}{3}\right)^x

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