Gaia is driving her truck from Paris to Lyon. The function D gives the total distance Gaia has driven (in kilometers) after t hours. What is the best interpretation for the following statement? The slope of the line tangent to the graph of D at t=3 is equal to 90 . Choose 1 answer: (A) During the first 3 hours, Gaia drove 90 kilometers per hour. B) At time 3, Gaia drove at a rate of 90 kilometers. (C) 3 hours after leaving, Gaia was 90 kilometers away from Paris. (D) 3 hours after leaving, Gaia drove at a rate of 90 kilometers per hour.

Question

Gaia is driving her truck from Paris to Lyon. The function  D gives the total distance Gaia has driven (in kilometers) after  t hours. What is the best interpretation for the following statement? The slope of the line tangent to the graph of  D at  t=3 is equal to 90 . Choose 1 answer: (A) During the first 3 hours, Gaia drove 90 kilometers per hour. B) At time 3, Gaia drove at a rate of 90 kilometers. (C) 3 hours after leaving, Gaia was 90 kilometers away from Paris. (D) 3 hours after leaving, Gaia drove at a rate of 90 kilometers per hour.

Bytelearn · Accepted Answer

Rate of Change Definition: The slope of a line tangent to a graph at a certain point represents the rate of change at that point.Speed Calculation: Since D represents total distance driven and t represents time, the slope represents the speed at time t.Tangent Line Slope at t=3: The statement says the slope of the line tangent to the graph of D at t=3 is equal to 90. This means at t=3, the speed is 90 kilometers per hour.

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