In a certain city the rate of taxation is the following: $x\%$ tax is collected for an income of $x$ thousand dollars. What income, in dollars, will yield the greatest take home pay? (Take-home pay is the income minus the tax on that income.)
\(\text{In a certain city the rate of taxation is the following: \\ $x\%$ tax is collected for an income of $x$ thousand dollars. \\ What income, in dollars, will yield the greatest take home pay? \\ (Take-home pay is the income minus the tax on that income.)}\)
+36915 Income x thousands tax = x * x%
Take home is x - x (x/100) = -x^2/100 + x Max will be at -b/2a = - 1/(2* (-1/100)) = 50 = x = $50 000
+36915 Income x thousands tax = x * x%
Take home is x - x (x/100) = -x^2/100 + x Max will be at -b/2a = - 1/(2* (-1/100)) = 50 = x = $50 000
