Growth Equations
Many times, we will wish to model growth of a population or of invested funds. To do this, we will usually use one of two models.
The first model is used primarily for calculating the interest earned on invested funds. We use the equation:
A(t) = P[1 + (r/n)] nt
where A(t) is the amount of money at time t. P is the principal or the initial amount of money. r is the interest rate expressed as a decimal. n is the number of times that interest is compounded per year and t is the time in years. This model is used if we have an investment that is compounded daily, weekly, monthly, semiannually, anually, etc.
Sometimes, interest is instead compounded continuously. In this case, we use the model:
A(t) = Pe rt
where A(t) is the amount at time t, P is the principal, r is the rate, and t is time. This model is also used to model the growth of populations as well as the decay of populations. If r > 0, then it is a model for growth. If r < 0, then it is a model for decay.
For these types of problems, you will normally be given all but one of the parameters and asked to find the last one. Sometimes, you will only be given that the population doubles or triples in a certain amount of time and not be given starting population. This might not seem like enough information, but it is because A(t) = cP for some number c, so plugging these values in, you will be able to divide by P and then use what you know about logs to find the other parameters.