Section 4.6: Modeling with Exponential Functions

1. Given the doubling / tripling / quadrupling time \(a\) of a population and the initial size of a population \(N_{0}\), develop a model for the population size as a function of time.
2. Given the relative growth rate \(r\) of a population and the initial size of a population \(N_{0}\), develop a model for the population size as a function of time.
3. Given an exponential model for a population, determine the amount of time it takes for the population to reach a certain population size.
4. Given the half-life \(h\) of a radioactive material and the amount of radioactive material present, develop a model for the amount of radioactive material as a function of time.
5. Given the proportion of radioactive material remaining in a sample relative to some starting time and the half-life \(h\) of the radioactive material, determine the amount of time that has passed since the starting time.
6. Given the temperature of an object above a given ambient temperature and a rate constant \(k\), develop a model for the temperature of the warmer object as a function of time.