Question

Describe three scenarios that involve a real-world linear or exponential function. At least one must be exponential. Identity whether your scenarios are linear or exponential. Provide an explanation to support your answers.

Answer 1

Three scenarios involving linear or exponential functions are population growth, compound interest, and radioactive decay.

Step-by-step explanation:

Scenario 1: Population Growth One scenario that involves an exponential function is population growth. When a population has unlimited resources, such as food and water, and ideal environmental conditions, it can exhibit exponential growth. As time passes, the population grows more rapidly, resulting in a J-shaped curve.

Scenario 2: Compound Interest An example of an exponential function is compound interest. When money is invested and earns interest that is compounded over time, the amount of money grows exponentially. The growth rate increases as the principal amount and the interest earned increase.

Scenario 3: Radioactive Decay Another scenario involving an exponential function is radioactive decay. The rate at which a substance decays is proportional to the amount of the substance present. This decay can be modeled by an exponential function, where the decay rate determines the rate of decrease.