3 Vocabulary Terms - Define/Illustrate
Name a situation that is exponential - involves exponents:
Write a table out if you have $100 and you gain 5% each year for 3 years:
Write a table out if you have $100 and you lose 5% each year for 3 years:
1. Exponential: In mathematics, exponential refers to a value that increases or decreases at an exponential rate, meaning it grows or declines at a consistent percentage over a fixed period of time. In the context of exponents, exponential refers to the operation of raising a number to a power.
2. Situation that is exponential: One example of a situation that is exponential is population growth. When a population grows exponentially, it means that the number of individuals in the population increases at a constant percentage over time, resulting in a rapid increase in population size. This growth pattern is often represented by an exponential function, such as the formula P(t) = P0 * e^(rt), where P0 represents the initial population size, r represents the growth rate, and t represents time.
3. Table for gaining 5% each year for 3 years:
Year | Amount
1 | $105
2 | $110.25
3 | $115.76
Each year, the amount increases by 5% of the previous year's amount. In this case, the initial amount of $100 is increased by 5% to $105 in the first year. Then, the new amount of $105 is increased by 5% to $110.25 in the second year, and so on.
4. Table for losing 5% each year for 3 years:
Year | Amount
1 | $95
2 | $90.25
3 | $85.74
Each year, the amount decreases by 5% of the previous year's amount. In this case, the initial amount of $100 is decreased by 5% to $95 in the first year. Then, the new amount of $95 is decreased by 5% to $90.25 in the second year, and so on.