Functions Involving Parameters, Vectors, and Matrices

Given that an investment's value over time follows the rational function modeled by $V(t) = \frac{1000}{1+9e^{-0.6t}}$, where $V(t)$ represents dollar value and $t$ years since initial investment, when will the investment first exceed $900$?

Which set represents a simple parametrization for the line $y=x$?

If the position of an object is given by the implicit equation $xy + \ln\left(\frac{y}{x}\right)=3$ where $x >0$ and $y>0$, which set of parametric equations best describes its motion if it follows the curve at constant horizontal velocity?

Given an ellipse defined by the equation $\frac{x^2}{9} + \frac{y^2}{16} = 1$, which parametric equations correctly describe this ellipse when parameterized by angle measure $t$?

If the function $f(x) = \frac{2x^3 - 8}{x - 2}$ is redefined at $x = 2$ to make it continuous, what should $f(2)$ equal?

Which pair of parametric equations corresponds to a particle's path described by $\frac{x^2}{9} + \frac{y^2}{16} = 1$ that ensures acceleration only in the vertical direction?

What is the parametric equation for a line that is collinear with the y-axis?

Given that $h(t)=t^3-6t$ defines $y$ in terms of $t$ for all real numbers, which parametric equation could represent $x$ as a function of $t$ to ensure that the graph of $y$ versus $x$ is continuous for all real values of $t$?

Given an implicitly defined function through the relation $xy = 6$, what parametrized expression for $y$ in terms of a new parameter 'a' will correctly describe its inverse?

What happens to the period and amplitude when a sinusoidal function $h(\theta) = m \cos(n\theta+c)+d$ is transformed into $H(\theta)=-m \cos(n\theta+c)+d$?