The real GDP per capita of sub-Saharan Africa (in 2009 U.S....

The real GDP per capita of sub-Saharan Africa (in 2009 U.S. dollars) from 1990 through 2030 is projected to be $$ f(t)=1.86251 t^{2}-28.08043 t+884 \quad(0 \leq t \leq 40) $$ where $t$ is measured in years, with $t=0$ corresponding to 1990 . a. What was the real GDP per capita of sub-Saharan Africa in $2000 ?$ b. Assuming that the projection holds true, what will be the GDP per capita of sub-Saharan Africa in 2030?

The real GDP per capita of sub-Saharan Africa (in 2009 U.S. dollars) from 1990 through 2030 is projected to be
$$
f(t)=1.86251 t^{2}-28.08043 t+884 \quad(0 \leq t \leq 40)
$$
where $t$ is measured in years, with $t=0$ corresponding to 1990 .
a. What was the real GDP per capita of sub-Saharan Africa in $2000 ?$
b. Assuming that the projection holds true, what will be the GDP per capita of sub-Saharan Africa in 2030?

Key Concepts

Function Evaluation and Substitution

Function evaluation involves determining the output of a function by substituting a specific value for its variable. This process is fundamental in mathematics and applied disciplines, as it allows one to obtain concrete results from abstract models. It is especially crucial when applying theoretical models to real-world data points.

Economic Projections

Economic projections use mathematical models to forecast future economic indicators, such as GDP per capita. These projections are essential for policy planning and analysis, as they translate historical data trends into predictions about future economic conditions. Understanding these projections helps in making informed decisions based on anticipated economic trends.

Polynomial Functions

Polynomial functions are algebraic expressions composed of variables and coefficients, where the variable is raised to a whole-number exponent. In many fields, including economics, they are used to model and analyze trends over time. The quadratic nature of a polynomial function, for example, can capture acceleration or deceleration in a trend, making it a useful tool for forecasting.

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