Exponential and Logarithmic Functions

Given an exponential function defined by $f(t)=Pe^{rt}$, where $P>0$ and $r<0$, what feature do these constraints on $P$ and $r$ guarantee about $f(t)$?

What is the first term of an arithmetic sequence with a common difference of 4, if its third term is 10?

If $f(x) = \frac{x^2 - x - 6}{x - 3}$ for all $x$ except $x = 3$, what kind of discontinuity exists at $x = 3$?

Which term best describes a function that can be drawn without lifting your pencil off of the paper for its entire domain?

What happens to the continuity of $f(x)$ if $\\lim_{x \\to c^{-}} f(x) \\neq \\lim_{x \\to c^{+}} f(x)$?

What is necessary for the piecewise function below to be continuous at x=3?

p(x)= $$\begin{cases} ax^{3}-b & ,\text{if } x <3 \\ cx+d & ,\text{if } x\geq3 \end{cases}$$

What is the next number in this arithmetic sequence? 12, 17, 22, ...

What unit is commonly used to measure angles in trigonometry?

What is the fifth term in the geometric sequence where the first term is 2, and the common ratio is -3?

If the graph of the quadratic function $f(x) = x^2$ is reflected over the x-axis and then vertically stretched by a factor of 3, what is the equation of the new function?