Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x {(x(t) = e^(2 t)),(y(t) = e^(

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Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x {(x(t) = e^(2 t)),(y(t) = e^(8 t)):}

y(x) =?

Guest Jun 4, 2015

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Best Answer

x = e^2t means ln(x) = 2t

y = e^8t means ln(y) = 8t

Therefore ln(y) = 4*ln(x) or ln(y) = ln(x⁴) or y = x⁴

Alternatively you could write directly: y = e^8t = (e^2t)⁴ = x⁴

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Alan Jun 4, 2015

Alan · Answer 1 · 2015-06-04T08:02:41

x = e^2t means ln(x) = 2t

y = e^8t means ln(y) = 8t

Therefore ln(y) = 4*ln(x) or ln(y) = ln(x⁴) or y = x⁴

Alternatively you could write directly: y = e^8t = (e^2t)⁴ = x⁴

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