Question

How do you write `x = e^t-1` and `y=e^2t` as a cartesian equation and then sketch the curve?

Answer 1

First of all I think that, maybe, there is a little mistake in your writing.

Doesn't the function is:

`x = e^t-1`
`y=e^(2t)`

instead of yours?

If I am right, than:

`x+1=e^trArrt=ln(x-1)` and

`y=e^(2ln(x+1))rArry=e^ln((x+1)^2)rArry=(x+1)^2`

(this is because: `e^lnf(x)=f(x)`)

And this is the equation of a parabola centered in `V(-1,0)` and that passes from the points `(0,+1)`, as you can see:

graph{(x+1)^2 [-10, 10, -5, 5]}

I hope that my hypotesis (of your little error of writing) is correct.