Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table below. Round parameters to the nearest thousandth.
$\begin{array}{|l|l|l|}
\hline x & -2 & 0 \
\hline y & 48 & 3 \
\hline
\end{array}$

A) $y = 3 e ^ { - 1.386 x }$
B) $y = - 1.386 e ^ { - 3 x }$
C) $y = - 3 e ^ { 1.386 x }$
D) $y = 3 e ^ { 1.386 x }$
E) $y = - 1.386 e ^ { 3 x }$

Question

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table below. Round parameters to the nearest thousandth.
$\begin{array}{|l|l|l|}
\hline x & -2 & 0 \
\hline y & 48 & 3 \
\hline
\end{array}$

A) $y = 3 e ^ { - 1.386 x }$
B) $y = - 1.386 e ^ { - 3 x }$
C) $y = - 3 e ^ { 1.386 x }$
D) $y = 3 e ^ { 1.386 x }$
E) $y = - 1.386 e ^ { 3 x }$

Quizplus · Accepted Answer

Using the point (0, 3), we find $a = 3$. Using the point (-2, 48), we can solve for $b$ in $48 = 3e^{b(-2)}$, which gives $b = -1.386$. Thus, the model is $y = 3e^{-1.386x}$.

Find the Exponential Model y=aebxy = a e ^ { b x }y=aebx

Find the Exponential Model $y = a e ^ { b x }$