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

A) $y$ is multiplied by $2.18$.
B) $2.18$ is added to $y$.
C) $1.31$ is added to $y$.
D) $y$ is multiplied by $1.31$.

Question

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

A) $y$ is multiplied by $2.18$. 
B) $2.18$ is added to $y$. 
C) $1.31$ is added to $y$. 
D) $y$ is multiplied by $1.31$.

Quizplus · Accepted Answer

In exponential regression, the equation takes the form $$y=a\cdot b^{t}$$ where $$a$$ is the initial value of $$y$$ and $$b$$ is the base, which determines how quickly the function grows or decays. Taking the derivative of this equation with respect to $$t$$ gives $$\frac{dy}{dt}=a\cdot b^{t}\cdot \ln(b)$$ So when $$t$$ is increased by 1 unit, we have $$\frac{dy}{dt}=y\cdot\ln(b)$$ which means that the percent change in $$y$$ is proportional to $$\ln(b)$$. In this problem, since the answer choices are all numbers, we can use the fact that $$\ln(2.18)\approx0.78$$ and $$\ln(1.31)\approx0.27$$ to determine that the correct answer is D. When $$t$$ is increased by 1 unit, $$y$$ is multiplied by the base, which is $$1.31$$ in this case.

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