Exponential and Logarithmic Functions

If an exponential function is described by $f(x) = a(b)^x$, what is $f(0)$?

When analyzing data using an exponential decay model $A(t) = A_0 imes e^{-rt}$, which variable in this model would you solve for to determine how quickly a substance is halving in quantity over time?

A certain radioactive substance decays at a rate of half its mass every century; if you start with a sample of pure substance weighing exactly one kilogram, what fraction of that kilogram remains undecayed after seven centuries according to an exponential decay model?

Which feature of an exponentiated quadratic equation $y = ae^{bx^2 + cx + d}$ indicates how sharply or broadly its parabolic shape stretches up or down?

How do you simplify the expression $(5^\eta)^{-?}$?

Which expression represents the division of two exponential terms $8^m$ divided by $8^n$?

In an exponentially growing bacterial culture that increases by a factor of $e$ each hour, which represents the approximate number of times the original amount will have been multiplied after five hours?

For which value of k does the function $g(x) = \frac{e^{kx} - e^{4}}{kx - 4}$ become continuous at $x=4$?

Given $h(x)=\ln|x-3|$, for what value(s) of 'a' would $\lim_{x \to a^{-}} h(x)$ not equal $\lim_{x \to a^{+}} h(x)$?

What must be true for c in order for $f(x)=\frac{ax+b}{cx+d}$, where $c \neq -\frac{d}{a}$, to not have any points of discontinuity?