The rate of depreciation dv / dt of a machine is inversely proportional to the square of t + 1, where v is the value of the machine t years after it was purchased. the initial value of the machine was $500,000, and its value decreased $200,000 in the first year. estimate its value to the nearest whole number after 6 years.

Question

Mathematics

Jocelyn Sanders

4 July, 11:23

The rate of depreciation dv / dt of a machine is inversely proportional to the square of t + 1, where v is the value of the machine t years after it was purchased. the initial value of the machine was $500,000, and its value decreased $200,000 in the first year. estimate its value to the nearest whole number after 6 years.

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Answers (2)

Know the Answer?

Elisabeth Horne · Answer 1

I think the answer for V6 is

V6 = 314285.71

Adonis Ellison · Answer 2

The solution for this problem is:

dV/dt = r / (t + 1) ², V (0) = $500000, V (1) = $500000 - $200000 = $300000

∫dV = r∫ 1 / (t + 1) ² dt

V (t) = - r / (t + 1) + C

500000 = - r / (0 + 1) + C

400000 = - r / (1 + 1) + C

C = 300000, r = - 100000

V (t) = 100000 / (t + 1) + 300000

V (6) = 100000 / (6 + 1) + 300000

V (6) = 14285.7143 + 300000

V (6) = $314285.71