Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table. $$\begin{array} { | c | c | c | }
\hline x & 0 & 3 \
\hline y & 6 & 1.5 \
\hline
\end{array}$$
A) $y = \frac { 1 } { 2 } e ^ { 0.6621 x }$
B) $y = e ^ { - 0.5621 x }$
C) $y = - e ^ { 0.4621 x }$
D) $y = 6 e ^ { - 0.4621 x }$
E) $y = 2 e ^ { 0.4621 x }$

Question

Find the exponential model $y = a e ^ { b x }$ that fits the points shown in the table. $$\begin{array} { | c | c | c | } 
\hline x & 0 & 3 \
\hline y & 6 & 1.5 \
\hline
\end{array}$$
A) $y = \frac { 1 } { 2 } e ^ { 0.6621 x }$
B) $y = e ^ { - 0.5621 x }$
C) $y = - e ^ { 0.4621 x }$
D) $y = 6 e ^ { - 0.4621 x }$
E) $y = 2 e ^ { 0.4621 x }$

Quizplus · Accepted Answer

Given the points (0, 6) and (3, 1.5), we can use the first point to find $a$ because when $x = 0$, $y = a e^{b \cdot 0} = a$. So, $a = 6$. To find $b$, we use the second point (3, 1.5): $1.5 = 6e^{3b}$. Solving for $b$, we get $b = -0.4621$. Thus, the correct model is $y = 6e^{-0.4621x}$.

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

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