Q. Mod 8, 10, 811Question 2 of 10 (1 point) | Question Attempt: 1 of 112345The table of ordered pairs (x,y) gives an exponential function. Write an equation for the function.\begin{tabular}{|c|c|}\hlinex & y \\\hline−1 & 24 \\\hline 0 & 6 \\\hline 1 & 23 \\\hline 2 & 83 \\\hline\end{tabular}
Observe Decreasing Y-values: Notice that the y-values are decreasing as the x-values increase, which is typical for an exponential decay function.
Find Base of Function: To find the base of the exponential function, look at the y-values when x increases by 1. Going from x=−1 to x=0, y decreases from 24 to 6.
Calculate Base Value: Calculate the base b by dividing the y-value at x=0 by the y-value at x=−1: b=246=41.
Confirm Base Calculation: Check the base with another pair of points. Going from x=0 to x=1, y decreases from 6 to 23. Calculate b=623=41 again, which confirms our base.
Write Exponential Function: Now, write the general form of the exponential function: y=a⋅bx. We already know b=41. To find a, use the point (0,6) because any number to the power of 0 is 1.
Determine Value of a: Plug x=0 and y=6 into the equation: 6=a×(41)0. Since (41)0=1, it follows that a=6.
Final Exponential Equation: Write the final equation of the exponential function: y=6×(41)x.
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