Imagine you are an assistant operations manager at a local logistics company. Your department is evaluating the depreciation of a fleet of delivery trucks over time. A finance team member provides you with a mathematical model where the value of a truck is projected using the exponential expression ${}0.82^t$, where $t$ represents the number of years since the truck was purchased.

To ensure your team understands the formula's mathematics before presenting it to the executive board, write a short, clear explanation of the mathematical components.

In your response, you must:

1. State the general algebraic definition of an algebraic base in an exponential expression and describe its role in repeated multiplication.
2. Identify the specific value that serves as the base in the expression ${}0.82^t$, and explain what this base indicates about how the truck's value changes each year.
3. Contrast the mathematical function of the base with the mathematical function of the exponent $t$ in this model.