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The exponential function t(x) increases at a rate of 30% through the ordered pair (0, –3) and is shifted down 7 units. What is the equation for the horizontal asymptote? y = –3 y = –7 y = 7 y = 0

User Natumsol
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The horizontal asymptote is y = -7.

The horizontal asymptote of an exponential function is determined by its vertical shift. If the function is shifted down n units, the horizontal asymptote will be y = -n. Therefore, in this case, the horizontal asymptote is y = -7.

Increase of 30%: The 30% increase tells us about the slope of the function in a specific region and doesn't directly affect the horizontal asymptote.

Ordered pair (0, -3): This point tells us about the initial value of the function, not its horizontal behavior as x approaches infinity or negative infinity.

Shifted down 7 units: Since the function is shifted down 7 units, its horizontal asymptote will also be shifted down by the same amount. Therefore, it will be at y = -7, not any of the other options.

The exponential function t(x) increases at a rate of 30% through the ordered pair-example-1
User Dom Vinyard
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