Chapter 11.1, Problem 49E

To determine

To determine: The correct option for the parametric curve to be identical to the graph of the function.

Answer to Problem 49E

The correct option is (C).

Explanation of Solution

Given information:

The parametric equations: $x=\ln \left(t\right)$ , $y=t$ for $t>0$

The options:

(A) $y=\ln x$ for all real x .

(B) $y={\ln }^x$ for $x>0$ .

(C) $y=e^x$ for all real x .

(D) $y=e^x$ for $x>0$

(E) $y=\ln \left(e^x\right)$ for $x>0$

Calculation:

The parametric equations are $x=\ln \left(t\right)$ and $y=t$ .

Substitute t for y in the equation $x=\ln \left(t\right)$ .

  $x=\ln y$

It is seen that x is negative for $0<y<1$ and x is positive for $1<y<\infty$ .

This means $y=e^x$ for all real x .

Hence, the correct option is (C).