What is the explicit formula for the curve $x=e^{0.1 t}, y=e^{t}, 0 \leq t \leq 1$ ?
A) $y=e^{10 x}$
B) $y=e^{0.1 x}$
C) $y=x e^{0.1}$
D) $y=x^{10}$

Name: What is the explicit formula for the curve $x=e^{0.1 t}, y=e^{t}, 0 \leq t \leq 1$ ? A) $y=e^{10 x}$ B) $y=e^{0.1 x}$ C) $y=x e^{0.1}$ D) $y=x^{10}$
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Question

Quizplus · Accepted Answer

To find the explicit formula, express $y$ in terms of $x$. Given $x = e^{0.1t}$, solve for $t$: $t = \frac{\ln x}{0.1}$. Substitute into $y = e^t$: $y = e^{\frac{\ln x}{0.1}} = x^{10}$.

What Is the Explicit Formula for the Curve x=e0.1t,y=et,0≤t≤1x=e^{0.1 t}, y=e^{t}, 0 \leq t \leq 1x=e0.1t,y=et,0≤t≤1

What Is the Explicit Formula for the Curve $x=e^{0.1 t}, y=e^{t}, 0 \leq t \leq 1$