The formula A=10 e^-0.003 t models the population of...

The formula $A=10 e^{-0.003 t}$ models the population of Hungary, $A,$ in millions, $t$ years after 2006.
a. Find Hungary’s population, in millions, for 2006, 2007, 2008, and 2009. Round to two decimal places.
b. Is Hungary’s population increasing or decreasing?

Key Concepts

Interpretation of Model Parameters

Interpretation of model parameters involves understanding the significance of constants like the initial value and the rate constant. In the context of exponential functions, the sign and magnitude of the rate constant help determine whether the process is characterized by growth or decay.

Rounding and Approximation

Rounding and approximation involve adjusting numerical results to a desired level of precision, such as rounding to two decimal places. This practice ensures that results are presented in a clear and standardized format for communication and analysis.

Evaluation of Functions

Evaluating functions involves substituting specific values into the equation to compute the outcome at those points. This process is crucial in obtaining numerical predictions from the model for given time intervals.

Population Modeling

Population modeling involves applying mathematical functions to predict changes in a population over time. Exponential functions are often employed because they can effectively describe constant proportional rates of change, whether the population is growing or declining.

Exponential Decay

Exponential decay is a specific type of exponential function where the constant k is negative, leading the quantity to decrease over time. This is commonly used in modeling populations, radioactive decay, or depreciation of assets.

Exponential Functions

Exponential functions are mathematical models of the form A = A?e^(kt) where A? is the initial amount and k is the constant rate of growth or decay. They are used to describe processes that change at a rate proportional to their current value.

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