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

A) $1.08$ is added to $y$
B) $1.17$ is added to $y$
C) $y$ is multiplied by $1.08$
D) $y$ is multiplied by $1.17$

Question

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

A) $1.08$ is added to $y$ 
B) $1.17$ is added to $y$ 
C) $y$ is multiplied by $1.08$ 
D) $y$ is multiplied by $1.17$

Quizplus · Accepted Answer

Exponential regression of the form $y = ab^t$ means that the value of $y$ is multiplied by the base $b$ each time $t$ increases by 1. Therefore, adding 1 to $t$ will result in $y$ being multiplied by $\text{base} + 1$ or $1 + r$ where $r$ is the growth rate. In this case, since the choices only provide options where a whole number is added to $y$, we can assume that the exponential regression is in the form $y = a(1+r)^t$ where the growth rate is a whole number percentage. Solving for the growth rate using the given options, we find that $1.08 \approx 8\%$ and $1.17 \approx 17\%$. Therefore, since adding 1 to $t$ results in an increase of $8\%$ or $1.08$ in $y$, the answer is C - $y$ is multiplied by $1.08$.

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