Module 2

• Slope gives us information about the changes of f(t) as t changes → speed and direction
• positive slope = increasing as t increases, negative slope = decreasing as t-increases. Zero slope - S(t) not changing
• The speed with which S(t) increases accelerates over time - because more individuals are reproducing per unit time as t increases
• discrete exponential growth formula: Formula: S(t) = S0g^t
• continuous exponetial growth formula: S(t) = S0e^(rt)
• S(t) →  population size at time t
• S0 → population size at time = 0
• g = number of offspring produced per discrete unit of time (year, month, day)
• r = number of offspring produced per individual per unit time
• derivative = model, function = solution
• what does the log function do: Gives us a sense of how big that number is/overall size of number (by telling us its order of magnitude)
• • For a series of numbers that changes by an order of magnitude at each step, log10 of those numbers will change by one at each step  (e.g everytime there is an extra x10, we go up 1 in log)
• exponential death formula: S(t) = S0e^-(ct)
• mean lifetime: 1/c
• c = number of disappearance events per capita per unit time
• r/c is the average number of offspring produced by an individual during its lifetime: 
• discrete data is data that can take on certain values e.g. integers/counts
• continuous is data that can take on any value within a certain range e.g. height