Final Answer:
The equation of the curve is y = k((1)/(2))^x, where k is a positive constant.
Step-by-step explanation:
The given equation is a power function equation, where the variable x is the exponent. A power function is a function of the form f(x) = ax^n, where a and n are constants, and n is not equal to zero. In the given equation, the constant a is equal to k/2, and the exponent n is equal to -1.
The power function equation can be graphed on the coordinate plane by plotting points. To plot points, substitute different values of x into the equation and calculate the corresponding values of y. For example, if x is equal to 0, then y is equal to k. If x is equal to 1, then y is equal to k/2. This continues for all the x-values, resulting in a graph with a decreasing slope.
The graph of the power function equation is a curve that starts at the point (0,k) and decreases as the x-values increase. The y-values decrease exponentially as the x-values increase, so the graph can be said to be exponentially decreasing.
The graph of the power function equation is a useful tool for understanding the behaviour of the equation. As the x-values increase, the y-values decrease at a faster and faster rate, which can be seen by the decreasing slope of the graph. This behaviour is due to the fact that the exponent in the equation is negative. As the exponent is negative, it causes the y-values to decrease exponentially as the x-values increase.
The power function equation is also useful for solving problems involving exponential or logarithmic functions. For example, the equation can be used to solve equations involving exponential growth or decay. By substituting different values of x into the equation, it is possible to solve for the corresponding values of y, which can then be used to solve the exponential equation.
In conclusion, the equation of the curve is y = k((1)/(2))^x, where k is a positive constant. The graph of the equation is a curve that starts at the point (0,k) and decreases exponentially as the x-values increase. The equation is useful for understanding the behaviour of exponential functions as well as for solving exponential equations.