Question

Which situations can be represented by an exponential function? Select each correct answer.

1) A toad population is increasing by about 7.5%
2) The value of a car decreases by 10% each year
3) The amount of money in a bank account grows by 5% each month
4) The temperature of a cooling cup of coffee decreases by 15% each minute

Answer 1

All the provided situations exemplify cases of exponential growth or decay, characterized by a consistent percent change over equal time periods, and thus can be modeled using exponential functions.

Step-by-step explanation:

Each of the given situations can be represented by an exponential function because they all describe scenarios where a quantity increases or decreases by a constant percentage over equal time intervals.

1. A toad population increasing by about 7.5% corresponds to exponential growth, where the population increases by a fixed percentage per time period.
2. The value of a car decreasing by 10% each year is a case of exponential decay, as the value diminishes by a constant percentage each year.
3. The amount of money in a bank account growing by 5% each month is another classic example of exponential growth, with the interest compounding over time.
4. The temperature of a cooling cup of coffee decreasing by 15% each minute is an example of exponential decay in a physical process, assuming the percentage decrease is constant.

In summary, if a quantity grows or decays by a constant percentage each time period, this can be modeled by an exponential function.