Ralph is 3 times as old as Sara. In 4 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now.
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Answer:
Step-by-step explanation:
From the table given in the question,
x y Difference Ratio
1 12 - -
2 36 36-12 = 24
3 108 108-36 = 72
4 324 324-108 = 216
5 972 972-324 = 648
There is a common ratio of 3 in each successive term.
Therefore, data given in the table will represent an exponential function.
For a point
------(1)
For another point of the table ,
--------(2)
Equation (2) divided by equation (1)
From equation (1),
Therefore, exponential function will be,
Given the next quadratic function:
to sketch its graph, first, we need to find its vertex. The x-coordinate of the vertex is found as follows:
where <em>a</em> and <em>b</em> are the first two coefficients of the quadratic function. Substituting with a = 2 and b = 3, we get:
The y-coordinate of the vertex is found by substituting the x-coordinate in the quadratic function, as follows:
The factorization indicates that the curve crosses the x-axis at the points (-2, 0) and (1/2, 0). We also know that the curve crosses the y-axis at (0,-2). Connecting these points and the vertex (-0.75, -3.125) with a U-shaped curve, we get:
