Q. Unit 7 Target 3 Writing Exponential E Algebra 1Write the equation for the exponential1.\begin{tabular}{|c|c|}\hlinex & y \\\hline−2 & −18 \\\hline−1 & −6 \\\hline 0 & −2 \\\hline 1 & −2/3 \\\hline\end{tabular}2.y=y=4.5.
Identify Pattern in y-values: Identify the pattern in the y-values to determine the base of the exponential function.y=a⋅bxWe see that when x increases by 1, y is multiplied by a constant factor.
Find Constant Factor: Find the constant factor by dividing a y-value by the previous y-value.(−6)/(−18)=31(−2)/(−6)=31(−32)/(−2)=31The constant factor is 31, so b=31.
Determine Initial Value: Use one of the points to find the initial value a. Let's use the point (0,−2). −2=a×(31)0−2=a×1 So, a=−2.
Write Final Exponential Equation: Write the final exponential equation using the values of a and b.y=−2×(31)x
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