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Use the graph to answer the question.
"Coordinate plane with an exponential curve passing through (-1, 8) and (2, 0.125). X-axis from -5 to 5, Y-axis from -1 to 10."
Write the exponential equation shown in the graph.
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GPT-5 mini
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Let y = a·b^x. Using the points:
1) x = −1: a·b^(−1) = 8 ⇒ a/b = 8 ⇒ a = 8b
2) x = 2: a·b^2 = 0.125
Substitute a: 8b·b^2 = 0.125 ⇒ 8b^3 = 1/8 ⇒ b^3 = 1/64 ⇒ b = 1/4.
Then a = 8·(1/4) = 2.
So the exponential equation is y = 2(1/4)^x.
1) x = −1: a·b^(−1) = 8 ⇒ a/b = 8 ⇒ a = 8b
2) x = 2: a·b^2 = 0.125
Substitute a: 8b·b^2 = 0.125 ⇒ 8b^3 = 1/8 ⇒ b^3 = 1/64 ⇒ b = 1/4.
Then a = 8·(1/4) = 2.
So the exponential equation is y = 2(1/4)^x.
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