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If y=38(1.04)xy=38(1.04)^x is graphed in the xyxy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) xx-intercept\newline(B) yy-intercept\newline(C) Slope\newline(D) The value yy approaches as xx becomes very large

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Full solution

Q. If y=38(1.04)xy=38(1.04)^x is graphed in the xyxy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) xx-intercept\newline(B) yy-intercept\newline(C) Slope\newline(D) The value yy approaches as xx becomes very large
  1. Identifying the characteristic: We need to identify which characteristic of the graph of the equation y=38(1.04)xy=38(1.04)^{x} is represented by a constant or coefficient in the equation itself.
  2. Finding the y-intercept: The y-intercept of a graph is the value of yy when xx is 00. Let's find the y-intercept of the given equation by setting xx to 00.y=38(1.04)0y = 38(1.04)^{0}
  3. Calculating the y-intercept: Since any number raised to the power of 00 is 11, we have:\newliney=38(1)y = 38(1)\newliney=38y = 38
  4. Interpreting the y-intercept: The value of yy when xx is 00 is 3838, which is a constant in the equation. This means that the y-intercept of the graph is 3838.
  5. Determining the x-intercept: The x-intercept is the value of xx when yy is 00. However, in the equation y=38(1.04)xy=38(1.04)^{x}, there is no value of xx that will make yy equal to 00 because the exponential function (1.04)x(1.04)^{x} is always positive and 3838 is a positive constant.
  6. Understanding the slope: The slope of a graph is represented by the coefficient of xx in a linear equation, which is not applicable here since this is an exponential function, not a linear one. Therefore, the slope is not a constant or coefficient in the equation.
  7. Analyzing the behavior as xx approaches infinity: The value yy approaches as xx becomes very large is related to the behavior of the exponential function as xx approaches infinity. In the equation y=38(1.04)xy=38(1.04)^{x}, as xx becomes very large, yy will also become very large. This is not a constant or coefficient in the equation.

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