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

A) $1.79$ is added to $y$
B) $7.65$ is added to $y$
C) $y$ is multiplied by $1.79$
D) $y$ is multiplied by $7.65$

Question

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

A) $1.79$ is added to $y$ 
B) $7.65$ is added to $y$ 
C) $y$ is multiplied by $1.79$ 
D) $y$ is multiplied by $7.65$

Quizplus · Accepted Answer

Exponential regression has the form $y=a \cdot b^t$, where $a$ and $b$ are constants. To determine what happens to $y$ when 1 is added to $t$, we can look at the exponent, which becomes $t+1$. Substituting into the equation gives:
$$y=a \cdot b^{t+1}=a \cdot b^t \cdot b$$
Since we want to know what happens to $y$ when 1 is added to $t$, we only need to consider the factor of $b$. If $b>1$, then multiplying by $b$ will increase the value of $y$, while if $0<b<1$, then multiplying by $b$ will decrease the value of $y$. In this question, we are not given the value of $b$, so we cannot tell which direction the change in $y$ will go. However, we are given the answer choices, which allow us to eliminate choices A and B, since those involve adding a constant to $y$, which has nothing to do with exponential regression. Thus, the correct answer is C, which involves multiplying $y$ by a constant, which is what happens when you change the exponent in an exponential function.

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