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If y=30((9)/(10))^(x) is graphed in the xy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation? Choose 1 answer: (A) Slope (B) The value y approaches as x decreases (C) x-intercept (D) y-intercept

If y=30(910)x y=30\left(\frac{9}{10}\right)^{x} is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) Slope\newlineB The value y y approaches as x x decreases\newline(C) x x -intercept\newline(D) y y -intercept

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Full solution

Q. If y=30(910)x y=30\left(\frac{9}{10}\right)^{x} is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) Slope\newlineB The value y y approaches as x x decreases\newline(C) x x -intercept\newline(D) y y -intercept
  1. Identify function type: Identify the type of function given by the equation y=30(910)xy=30\left(\frac{9}{10}\right)^x. This is an exponential function of the form y=a(b)xy=a(b)^x, where aa is the initial value and bb is the base of the exponential.
  2. Determine y-intercept: Determine the y-intercept of the graph.\newlineThe y-intercept occurs when x=0x=0. Plugging x=0x=0 into the equation, we get y=30(910)0=30(1)=30y=30\left(\frac{9}{10}\right)^0 = 30(1) = 30. This shows that the y-intercept is 3030, which is the coefficient of the exponential expression in the equation.
  3. Analyze other options: Analyze the other options to confirm that they are not constants or coefficients in the equation.\newline(A) Slope: The slope is not constant in an exponential function; it changes at every point on the graph.\newline(B) The value yy approaches as xx decreases: This would be the horizontal asymptote, which is not explicitly given in the equation.\newline(C) xx-intercept: The xx-intercept is not given by a constant or coefficient in the equation; it would require setting yy to 00 and solving for xx, which is not straightforward in this case.
  4. Conclude characteristic in equation: Conclude which characteristic of the graph is displayed as a constant or coefficient in the equation.\newlineThe yy-intercept is the only characteristic given as a constant or coefficient in the equation, which is 3030.

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