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.
-$$y = 700 ( 1.9 ) ^ { x }$$
A) $y = 700 e ^ { x } \ln 1.9 , y = 700 e ^ { 0.642 x }$
B) $y = 1.9 e ^ { x } \ln 700 , y = 1.9 e ^ { 6.551 x }$
C) $\mathrm { y } = 700 \mathrm { e } ^ { 1.9 x } , \mathrm { y } = 7002.718 ^ { 0.642 \mathrm { x } }$
D) $y = ( \ln 700 ) \mathrm { e } ^ { \mathrm { x } \ln 1.9 } , \mathrm { y } = 6.551 \mathrm { e } ^ { 0.642 \mathrm { x } }$

Question

Quizplus · Accepted Answer

The equation $y = 700(1.9)^x$ can be rewritten using the property that $a^b = e^{b\ln a}$, resulting in $y = 700e^{x\ln 1.9}$. Rounding $\ln 1.9$ to three decimal places gives approximately 0.642, so the equation becomes $y = 700e^{0.642x}$.

Choose the One Alternative That Best Completes the Statement or Answers