Mathematics - Calculus - Applications of Integration
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It is estimated that x years from now, the value V(x) of an acre of farmland will be increasing at the rate of V'(x) = 0.4x^3 / square root of 0.2x^4 + 8,000 dollars per year. The land is currently worth $500 per acre.
a) FInd V(x)
b) How much will the land be worth in 10 years?
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(a) V'(x) = [0.4x^3 / {square root of (0.2x^4 + 8,000)}]. First we integrate V'(x).dx.
Let 0.2x^4 + 8000 = u. Differentiating, we get, ...
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