Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. $$\begin{array} { | l | l | l | }
\hline x & 0 & 4 \
\hline y & 25 & 5 \
\hline
\end{array}$$
A) $y = 25 e ^ { - 0.4024 x }$
B) $y = 25 e ^ { 0.5024 x }$
C) $y = - \frac { 1 } { 25 } e ^ { 0.4024 x }$
D) $y = \frac { 1 } { 25 } e ^ { - 0.6024 x }$
E) $y = - \frac { 1 } { 25 } e ^ { - 0.4024 x }$

Question

Find the exponential model that $y = a e ^ { b x }$ fits the points shown in the table. $$\begin{array} { | l | l | l | } 
\hline x & 0 & 4 \
\hline y & 25 & 5 \
\hline
\end{array}$$ 
A) $y = 25 e ^ { - 0.4024 x }$
B) $y = 25 e ^ { 0.5024 x }$
C) $y = - \frac { 1 } { 25 } e ^ { 0.4024 x }$
D) $y = \frac { 1 } { 25 } e ^ { - 0.6024 x }$
E) $y = - \frac { 1 } { 25 } e ^ { - 0.4024 x }$

Quizplus · Accepted Answer

Given the points (0, 25) and (4, 5), we can use the first point to find $a$ because when $x=0$, $y=a$. Thus, $a=25$. Using the second point (4, 5) and the value of $a$, we can solve for $b$ in the equation $5 = 25e^{4b}$. Simplifying gives $e^{4b} = \frac{1}{5}$, and solving for $b$ gives $b \approx -0.4024$. Therefore, the correct model is $y = 25e^{-0.4024x}$.

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

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