Exponential and Logarithmic Functions

Which expression determines whether there exists an infinite limit approaching positive infinity for $f(x) = \log_7(x^2 - x - 12)$?

Which equation represents a logarithmic decay model?

If the population of a certain species of fish decreases by 12% each year, which function type best models this situation?

When modeling data with a logarithmic trend, which equation would you use to predict the value of y when x is increased tenfold?

If the population of a certain bacteria culture doubles every 3 hours, which logarithmic function represents the time $t$ in hours it takes for the population to reach $P$ if the initial population is $P_0$?

If the population of a city is modeled by the function $P(t) = 1000(2)^t$, where $t$ is time in years, after how many years will the population reach 8000?

Given $h(t) = \log_{5}(t^{2} -4)$, which value represents an asymptote for this transformed logarithmic function?

What is the base of the common logarithm?

In modeling population growth using an exponential function $P(t)=P_0e^{rt}$, with $P_0$ being initial population and $r$ being growth rate, what logarithmic equation would you use to find how long it takes for population to double?

What does it mean if a function is continuous at a point x = c?