Question

can you please help me with number 2 and 3? thanks

Problem 2. Consider a version of question 9 from the first WebWork problem set and an attempt at solving it. Find and explain the 3 mistakes that were made. Use the line numbers to identify where they occurred. Question 9: If a (base 10) double-log plot displays a line through the points (-3, -2) and (5,5), find the relation between x and y. Solution attempt: First, a correct double-log plot is sketched. Then, we set out to write the equation of the line on that plot: log(y) = m.log(x) + b (1) log(y) = 5- (-2) .log(x) + b (2) 5-(-3) log(y) = 7/8.log() + b Now, to find b, we plug in a point we know to be on the line: (5,5). log(5) = 7/8.log(5) + b b=1/8 log(5) (5) This gives us the following equation, which we will exponentiate to remove the logs. log(x) = log() . 7/8 + log(5) 1/8 (6) y = 104(a) 7/8 + 100(8):1/8 7 + 5. 1 (7) (8) 8 72 8

Answer 1

TH Given points: (-3,-2) and (5,5) Equation of the line: log(y) = m-log(x) + 5-(-2), log(y) = log(x) +B 5-(-3) That is, we get log(y)= 10g(x)+6 (1) To find h, we plus in a point we know to be on the line: (5,5) Then, we get log(5) = -log(5) + - 108(5) +6 => b=10(9)-1000) log(5) b = 108(5) Substituting b = 5105(5) in equation (1), we get log(y) = 109(x)+310869) log(y) = log(x)+10g (518) [1og(**) = nlog(x)] log(y) = log(***)(518) = 1 7 y = 10 de{*Yske) y=(x?*)(518) Therefore, y= (5x?)** 1/8