The gross domestic product (GDP) of the United States, in...

The gross domestic product (GDP) of the United States, in trillions of dollars, from 2011 through 2015 is approximately $$ G(t)=0.064 t^{2}+0.473 t+15.0 \quad(0 \leq t \leq 4) $$ where $t$ is measured in years, with $t=0$ corresponding to $2011 .$ In constructing this model, the government used actual GDP figures from 2011 and 2012 and estimates for the years 2013 through 2015. a. What was the U.S. GDP in 2011? b. What is the predicted U.S. GDP for $2015 ?$

The gross domestic product (GDP) of the United States, in trillions of dollars, from 2011 through 2015 is approximately
$$
G(t)=0.064 t^{2}+0.473 t+15.0 \quad(0 \leq t \leq 4)
$$
where $t$ is measured in years, with $t=0$ corresponding to $2011 .$ In constructing this model, the government used actual GDP figures from 2011 and 2012 and estimates for the years 2013 through 2015.
a. What was the U.S. GDP in 2011?
b. What is the predicted U.S. GDP for $2015 ?$

Key Concepts

Gross Domestic Product (GDP)

GDP is an economic indicator that measures the total value of all goods and services produced over a specific time period. It serves as a comprehensive scorecard of a country’s economic health, often used for comparison over time or between different countries.

Mathematical Modeling in Economics

Mathematical modeling involves using functions to represent real-world economic phenomena. In this context, a polynomial function is used to model GDP over time, combining actual data with estimates to reflect observed trends and predict future values.

Function Evaluation

Function evaluation is the process of computing the output of a function for a given input by substituting the input value into the function. This concept is crucial for translating the model into concrete predictions, such as calculating GDP for specific years.

Domain and Variable Interpretation

In the context of modeling, the domain defines the allowable inputs for the function. Interpreting the variable correctly—for instance, linking the numerical value to a particular year—is essential for ensuring that the function is applied accurately in a real-world scenario.

Extrapolation in Economic Forecasting

Extrapolation is the method of predicting values outside the range of observed data using an established model. This technique is commonly used in economic forecasting to estimate future trends based on current and historical data.

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