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 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 points2500.4500.
Solution
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The value of the office equipment depreciates linearly from 2,000 over 10 years. This means that each year, the value decreases by (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.
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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 to produce 30 units of the craft.
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