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Office equipment was purchased for $20,000 and will have a scrap value of $2,000 after 10 years.  If its value is depreciated linearly, find the linear equation that relates value (V) in dollars to time (t) in years: *10 pointsV(t) = 1,800t - 20,000.V(t) = 1,800t + 20,000.V(t) = –1,800t + 20,000.V(t) = –1,800t - 20,000.2.  Suppose you are running a small business that produces handmade crafts. The total cost (C) to produce x units of your craft is given by the equation C=50x+2000, where C is in dollars. Determine the total cost of producing 30 units and interpret the result.*10 points$1500.$2500.$3500.$4500.

Question

Office equipment was purchased for 20,000andwillhaveascrapvalueof20,000 and will have a scrap value of 2,000 after 10 years.  If its value is depreciated linearly, find the linear equation that relates value (V) in dollars to time (t) in years: *10 pointsV(t) = 1,800t - 20,000.V(t) = 1,800t + 20,000.V(t) = –1,800t + 20,000.V(t) = –1,800t - 20,000.2.  Suppose you are running a small business that produces handmade crafts. The total cost (C) to produce x units of your craft is given by the equation C=50x+2000, where C is in dollars. Determine the total cost of producing 30 units and interpret the result.*10 points1500.1500.2500.3500.3500.4500.

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Solution

  1. The value of the office equipment depreciates linearly from 20,000to20,000 to 2,000 over 10 years. This means that each year, the value decreases by (20,00020,000 - 2,000) / 10 = $1,800. Since the value decreases, the slope of the linear equation is negative. Therefore, the equation that represents the value of the office equipment over time is V(t) = -1,800t + 20,000.

  2. The total cost (C) to produce x units of your craft is given by the equation C=50x+2000. To find the total cost of producing 30 units, substitute x = 30 into the equation: C = 50*30 + 2000 = 3500.Thismeansthatitcosts3500. This means that it costs 3500 to produce 30 units of the craft.

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