Use exponential regression to determine what happens to $y$ when t is increased by 1 unit.

A) $y$ is multiplied by 2 .
B) 2 is added to $y$.
C) $1.34$ is added to $y$.
D) $\quad y$ is multiplied by $1.34$.

Question

Use exponential regression to determine what happens to $y$ when t is increased by 1 unit.

A) $y$ is multiplied by 2 . 
B) 2 is added to $y$. 
C) $1.34$ is added to $y$. 
D) $\quad y$ is multiplied by $1.34$.

Quizplus · Accepted Answer

Exponential regression models are of the form $y=a\cdot b^t$ where $a$ and $b$ are constants. Taking the derivative with respect to $t$ gives $\frac{dy}{dt}=a\cdot b^t\cdot \ln(b)$. This means that the change in $y$ for a 1 unit increase in $t$ is proportional to the current value of $y$, with a proportionality constant of $\ln(b)$. In other words, the value of the function is multiplied by the factor of $\ln(b)$ each time the input is increased by 1. Since option D implies multiplication of $y$ by a factor of $1.34$, the correct answer is D.

Use Exponential Regression to Determine What Happens To yyy When T Is Increased by 1 Unit

Use Exponential Regression to Determine What Happens To $y$ When T Is Increased by 1 Unit