In 1990 the average family income was about 39000, and in 2000 it was about 65124 .
Let $x=0$ represent 1990, $x=1$ represent 1991, and so on. Find values for $a$ and $b$ (rounded to one decimal place if necessary) so that $f(x)=a x+b$ models the data
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b=
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What was the average family income in 1995 ?
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Answer
Final Answer: The values for a and b that model the data are \(a = \boxed{2612.4}\) and \(b = \boxed{39000}\). The average family income in 1995 was \(\boxed{\$52062.0}\).
Step 1 ：Given the data points (0, 39000) and (10, 65124), we can find the slope (a) and y-intercept (b) of the line.
Step 2 ：The slope of a line is given by the formula \((y2 - y1) / (x2 - x1)\). Substituting the given points into this formula, we get \(a = (65124 - 39000) / (10 - 0) = 2612.4\).
Step 3 ：The y-intercept is the value of y when x = 0, which is given as 39000. So, \(b = 39000\).
Step 4 ：Thus, the linear model that fits the data is \(f(x) = 2612.4x + 39000\).
Step 5 ：To find the average family income in 1995, we substitute x = 5 (representing 1995) into the equation. This gives us \(f(5) = 2612.4*5 + 39000 = 52062.0\).
Step 6 ：Final Answer: The values for a and b that model the data are \(a = \boxed{2612.4}\) and \(b = \boxed{39000}\). The average family income in 1995 was \(\boxed{\$52062.0}\).
