Use exponential regression to determine what happens to $y$ when 1 is added to t.

A) $y$ is multiplied by $0.89$.
B) $\quad y$ is multiplied by $0.73$.
C) $0.73$ is added to $y$.
D) $0.89$ is added to $y$.

Question

Use exponential regression to determine what happens to $y$ when 1 is added to t.

A) $y$ is multiplied by $0.89$. 
B) $\quad y$ is multiplied by $0.73$. 
C) $0.73$ is added to $y$. 
D) $0.89$ is added to $y$.

Quizplus · Accepted Answer

Exponential regression models have the form $y=a\cdot b^t$, where $a$ and $b$ are constants. Taking the derivative of this function with respect to $t$ gives $y'=a\cdot b^t\ln b$. Therefore, $\frac{dy}{dt}$ is proportional to $y$ (i.e. $\frac{dy}{dt}$ is some constant times $y$). This means that the function is of the form $y=ce^{kt}$, where $k$ is a constant. Taking the derivative of this function with respect to $t$ gives $\frac{dy}{dt}=kce^{kt}$, which is proportional to $y=ce^{kt}$ (i.e. $\frac{dy}{dt}$ is some constant times $y$). Therefore, adding 1 to $t$ will multiply $y$ by some constant, and the only answer choice that reflects this is A.

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