Question 1

Given the parametric equations $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, which of the following is the correct Cartesian equation relating x$ and y$?

Accepted Answer

$$x = y + 1$$

Question 2

If $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, what is the value of x$ when y = 1$?

Accepted Answer

$$x = 2$$

Question 3

For the parametric equations $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, what is the value of t$ when x = 3$?

Accepted Answer

$$t = \frac{1}{4} \ln(2)$$

Question 4

Which of the following best describes the graph of the Cartesian equation $$x = y + 1$$?

Accepted Answer

A straight line with slope 1 and $$y-$$intercept 1

Question 5

Suppose a population grows according to $$y = e$$^{4t}$$, where t$ is measured in years. If the initial population is 1, what will the population be after 2 years?

Accepted Answer

$$y = e$$^{8}$$

Question 6

Given $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, which of the following is the correct expression for t$ in terms of y$?

Accepted Answer

$$t = \frac{1}{4} \ln(y)$$

Question 7

If $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, what is the value of y$ when x = 5$?

Accepted Answer

$$y = 4$$

Question 8

A scientist models the concentration of a chemical as $$y = e$$^{4t}$$, and the total amount as x$$ = $$e^{4t} + 1$. What is the difference between the total amount and the concentration after t$ years?

Accepted Answer

$$1$$

Question 9

Which of the following statements is true about the parametric curve defined by $$x = e$$^{4t}$$ + 1$$, $$y = e$$^{4t}$$ for t$$ \in \mathbb{R}$$?

Accepted Answer

The curve lies entirely to the right of $$x = 1$$

Question 10

If $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, what is the x$-intercept of the Cartesian equation?

Accepted Answer

$$x = 1$$

Question 11

Given the parametric equations $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, which of the following is the correct inverse relationship for y$ in terms of x$?

Accepted Answer

$$y = x - 1$$

Question 12

A medical researcher uses the model $$y = e$$^{4t}$$ for the growth of bacteria, and x$$ = $$e^{4t} + 1$ for the total count including a baseline. If the baseline is removed, what is the new total count after t$ hours?

Accepted Answer

$$y$$

Question 13

If $$x = e$$^{4t}$$ + 1$$ and $$y = e$$^{4t}$$, what is the value of t$ when y = 0$?

Accepted Answer

$$t$$ does not exist

Question 14

Which of the following best describes the domain of the Cartesian equation $$x = y + 1$$ derived from the parametric equations $$x = e$$^{4t}$$ + 1$$, $$y = e$$^{4t}$$?

Accepted Answer

$$y \u003e 0$$

Parametric and Cartesian Equations: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards