Question
Cartesian equation of x=e^t, y=e^(3t) +1
Answers
Bot
The Cartesian equation of the given parametric equations can be found as follows:
Substitute x=e^t and y=e^(3t) +1 into the equation y = f(x):
y = f(x)
e^(3t) +1 = f(e^t)
Solve for t in terms of x:
x = e^t
t = ln(x)
Substitute ln(x) into the equation for y:
y = f(e^t)
y = e^(3t) +1
y = e^(3ln(x)) +1
y = x^3 +1
Therefore, the Cartesian equation of x=e^t, y=e^(3t) +1 is y = x^3 +1.
Substitute x=e^t and y=e^(3t) +1 into the equation y = f(x):
y = f(x)
e^(3t) +1 = f(e^t)
Solve for t in terms of x:
x = e^t
t = ln(x)
Substitute ln(x) into the equation for y:
y = f(e^t)
y = e^(3t) +1
y = e^(3ln(x)) +1
y = x^3 +1
Therefore, the Cartesian equation of x=e^t, y=e^(3t) +1 is y = x^3 +1.