Daily oil imports to the United States from Mexico can be...

Daily oil imports to the United States from Mexico can be approximated by $$ I(t)=-0.015 t^{2}+0.1 t+1.4 $$ million barrels $/$ day $(0 \leq t \leq 8)$ where $t$ is time in years since the start of $2000 .^{2}$ According to the model, in what year were oil imports to the United States greatest? How many barrels per day were imported that year? HINT [See Example 1.]

Daily oil imports to the United States from Mexico can be approximated by
$$
I(t)=-0.015 t^{2}+0.1 t+1.4
$$
million barrels $/$ day $(0 \leq t \leq 8)$ where $t$ is time in years since the start of $2000 .^{2}$ According to the model, in what year were oil imports to the United States greatest? How many barrels per day were imported that year? HINT [See Example 1.]

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Applied Mathematical Modeling

Applied mathematical modeling involves using mathematical functions to represent and analyze real-world scenarios. In this context, interpreting the vertex of the function in relation to time helps determine the specific time (such as a particular year) when an event reaches its peak value, and the corresponding function value represents the magnitude of the event.

Quadratic Functions

A quadratic function is a second-degree polynomial expressed in the form ax² + bx + c. Such functions produce parabolic graphs and are widely used in modeling situations where there is an optimum value (maximum or minimum), such as in certain economic, physical, or natural processes.

Vertex of a Parabola

The vertex of a parabola represents the maximum or minimum point of a quadratic function. When the coefficient of the squared term is negative, the parabola opens downward, and the vertex is its highest point. The t-coordinate of the vertex can be calculated using the formula -b/(2a), which is key to identifying the time at which the maximum value occurs, and substituting it back into the function yields the maximum value.

Transcript

Please give Ace some feedback