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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?

User Ewizard
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Final answer:

The equation for the horizontal asymptote of the exponential function is y = -7.

Step-by-step explanation:

The equation for the horizontal asymptote of the exponential function (t(x)) can be found by considering the behavior of the function as x approaches positive or negative infinity. In this case, the function increases at a rate of 30% through the ordered pair (0, -3) and is shifted down 7 units. The equation for the horizontal asymptote can be determined by finding the value that the function approaches as x goes to infinity or negative infinity.

To find the equation for the horizontal asymptote, we first need to determine the growth factor of the function. Since the function increases at a rate of 30%, the growth factor is 1 + 30% = 1.30. Next, we need to find the vertical shift of the function. Since the function is shifted down 7 units, the equation for the horizontal asymptote will be y = -7. Therefore, the equation for the horizontal asymptote is y = -7.

User Unbreak
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