Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table below. Round parameters to the nearest thousandth.
$\begin{array}{|c|c|c|}
\hline x & 0 & 1 \
\hline y & 5 & 10 \
\hline
\end{array}$

A) $y = 5 e ^ { 0.693 x }$
B) $y = 0.693 e ^ { - 5 x }$
C) $y = - 5 e ^ { - 0.693 x }$
D) $y = 5 e ^ { - 0.693 x }$
E) $y = 0.693 e ^ { 5 x }$

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.
$\begin{array}{|c|c|c|}
\hline x & 0 & 1 \
\hline y & 5 & 10 \
\hline
\end{array}$

A) $y = 5 e ^ { 0.693 x }$
B) $y = 0.693 e ^ { - 5 x }$
C) $y = - 5 e ^ { - 0.693 x }$
D) $y = 5 e ^ { - 0.693 x }$
E) $y = 0.693 e ^ { 5 x }$

Quizplus · Accepted Answer

Given the points (0, 5) and (1, 10), we can substitute these into the exponential model $y = a e ^ { b x }$. For the point (0, 5), we get $5 = a e^{b \cdot 0}$, which simplifies to $5 = a$, since $e^0 = 1$. For the point (1, 10), we substitute $x = 1$ and $y = 10$ into the model, getting $10 = 5e^b$. Solving for $b$, we find $b = \ln(2) \approx 0.693$. Therefore, the model is $y = 5 e ^ { 0.693 x }$.

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