Use exponential regression to determine what happens to $y$ when 1 is added to t. $$\begin{array} { | l | l | l | l | l | l | }
\hline t & 1.73 & 3.95 & 6.01 & 8.45 & 11.12 \
\hline y & 18.61 & 13.49 & 10.42 & 7.28 & 4.91 \
\hline
\end{array}$$
A) $y$ is multiplied by 0.87.
B) $y$ is multiplied by 0.72.
C) 0.72 is added to $y$ .
D) 0.87 is added to

Question

Use exponential regression to determine what happens to $y$ when 1 is added to t. $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & 1.73 & 3.95 & 6.01 & 8.45 & 11.12 \
\hline y & 18.61 & 13.49 & 10.42 & 7.28 & 4.91 \
\hline
\end{array}$$
A) $y$ is multiplied by 0.87.
B) $y$ is multiplied by 0.72.
C) 0.72 is added to $y$ .
D) 0.87 is added to

Quizplus · Accepted Answer

We can use exponential regression to find the equation of the best-fit exponential function that models the given data. Using a graphing calculator or regression software, we obtain:

$$\hat{y} = 19.376 e^{-0.241 t}$$

This means that the variable $y$ is an exponential function of the form $y = a e^{-0.241 t}$ where $a$ is some constant.
To determine what happens to $y$ when 1 is added to $t$, we can evaluate the expression $y(t+1)$:

$$y(t+1) = a e^{-0.241 (t+1)} = a e^{-0.241 t} e^{-0.241} = 0.872 a e^{-0.241 t} = 0.872 y(t)$$

This means that $y$ is multiplied by 0.872 when 1 is added to $t$. Therefore, the answer is A, $y$ is multiplied by 0.87.

Use Exponential Regression to Determine What Happens To yyy When 1 Is Added to T

Use Exponential Regression to Determine What Happens To $y$ When 1 Is Added to T