Final answer:
The function f(t) = 5450(0.89)ᵗ represents a yearly percent decrease of 11% in the value it models, because the base of the exponential function, 0.89, is less than one.
Step-by-step explanation:
Understanding Percent Change in Functions
The function in question is f(t) = 5450(0.89)ᵗ, where t represents years. To describe the percent change of this function, we must understand the structure of the exponential function. The base, 0.89, is less than one, indicating a yearly percent decrease. The percent change can be found by subtracting the base from one and then converting that difference to a percentage.
To calculate the percent change:
1 - 0.89 = 0.11 or 11%. This means the function depicts an annual decrease of 11%. Another way to interpret this is that the quantity represented by the function f(t) decreases to 89% of its previous year's value every year, which is a depreciation or decay at an annual rate of 11%.
In the context of the provided data points from various sources, such as the graph showing the percent change at the annual rate of certain economic indicators across years and the equation examples for future value and cost of living adjustments, the concept of percent change remains consistent. It represents the rate at which a value grows or declines over a period, usually a year. In the function given, the negative exponent indicates a decline rather than growth.
In conclusion, f(t) models a consistent yearly percent decline of 11%, which can be significant when projecting values over multiple years. This steady rate of decrease would ultimately lead to diminishing values over time.