A manufacturer buys 55000$ worth of machinery that depreciates linearly so that its trade-in value after 10 years will be 2500$.a) Express the value of the machinery depending on its age.b) Sketch the graph of the dependence.c) When does the machinery become worthless?
y = mx +b 55000 -2500 = 52500 ... so the machinery depreciates 52500 dollars every 10 years. The slope is -52500/10 or -5250/1 or -5250 y = -5250x +55000 You have to use the equation to sketch the line. Use very large scales. Start at 55000 up the y- axis go down 5250 and over to the right 1. make a point. Connect the two points and keep going that is your line. The machine will become worthless when the line intersects the x-axis. or algebraically when y = 0 0 = -5250x +55000 -55000 = -5250x x = 10.476 The machinery will become worthless in about 10.5 years.
Let x = 0 (in years) be the price of when he first got the macinery. That means when x = 0, the cost is $55,000 and that when x = 10, the cost is $2,500. Since this function is linear, we can express it in the form of: y = mx + b So we can derive: 55000 = m(0) + b == b = 55000 2500 = m(10) + b == 10m + b = 2500 Since the previous one stated that b = 55000, plug it into the second. 10m + b = 2500 == 10m + 55000 = 2500 == 10m = -52500 == m = -5250 So we have the following function. F(x) = -5250x + 55000 When this becomes worthless, I assume you mean when F(x) = 0. -5250x + 55000 = 0 == -5250x = -55000 == x = 5500/525 ≈ 10.48 So after 11 years, it will be worthless. Hope this helps!
