eliminate the parameter to find the cartesian equation of the curve for x=e^t, y=e^-5t.

Answer 1

We want to eliminate the parameter t and write y in terms of x.

From the given equations, we have:

x = e^t
y = e^(-5t)

Taking the natural logarithm of both sides of the first equation, we get:

ln(x) = t

Substituting this expression for t in the second equation, we get:

y = e^(-5 ln(x))
y = x^(-5)

Therefore, the Cartesian equation of the curve is y = x^(-5).

Answer 2

or,
y = e^(-5t) = (e^t)^-5 = x^-5