Question

1. Describe two different situations that could be modelled by an exponential function. 2. Clearly define all variables in the relationship. 3. Interpret the growth or decay factor and the initial amount, which cannot be 1. 4. Explain why this type of function makes sense as a model for these real applications, by referring to key features of this function. 5. Your justification should also include reference to at least two of graphical, numeric, and/or algebraic models.

Answer 1

1. Population decay can be modelled using the exponential function. Let's say a small pond has a fish population of 160. Each day the population reduces to half that of previous day's population. At the end of the week, the fish population would be 1.25 .
   
   Use the exponential formula and realize that and , which are respectively the initial population and decay factor. This equation models our situation aptly and can be utilized in large scale applications to obtain or predict the results.
2. Compound interest can be also modelled using exponential growth function. Let $4000 compounds annually at an interest rate 6%. Let x be the time in years and y be the total money accumulated.
   
   Now, gives the solution. Here, 4000 is the initial investment, x is the number of years and 1.06 is the growth factor of investment.