Choose the one alternative that best completes the statement or answers the question.
Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three
decimal places.
-$$y = 4 ( 3 ) ^ { x }$$
A) $\mathrm { y } = 4 \mathrm { e } ^ { \mathrm { x } \ln 3 } , \mathrm { y } = 4 \mathrm { e } ^ { 1.099 \mathrm { x } }$
B) $\mathrm { y } = 3 \mathrm { e } ^ { \mathrm { x } \ln 4 } , \mathrm { y } = 3 \mathrm { e } ^ { 1.386 \mathrm { x } }$
C) $\mathrm { y } = 4 \mathrm { e } ^ { 3 \mathrm { x } } , \mathrm { y } = 42.718 ^ { 1.099 \mathrm { x } }$
D) $y = ( \ln 4 ) \mathrm { e } ^ { \mathrm { x } \ln 3 } , \mathrm { y } = 1.386 \mathrm { e } ^ { 1.099 \mathrm { x } }$

Question

Quizplus · Accepted Answer

The equation $y = 4(3)^x$ can be rewritten using the base $e$ by expressing $3^x$ as $e^{x\ln(3)}$. Therefore, $y = 4e^{x\ln(3)}$. Rounding $\ln(3)$ to three decimal places gives approximately $1.099$, so the equation becomes $y = 4e^{1.099x}$.

Choose the One Alternative That Best Completes the Statement or Answers