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 can determine that $a = 3$ because when $x = 0$, $y = a e^{b\cdot0} = a$. To find $b$, we use the point (-2, 48) and the already determined $a = 3$, leading to the equation $48 = 3e^{b(-2)}$. Solving for $b$ gives $b = -1.386$, thus the model is $y = 3e^{-1.386x}$.

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