11 Laura is taking a road trip to a destination that's 250 miles away. She decides to model her trip with the distance function d(t)=55 t+10 to predict how far she'll have driven after t hours. In this scenario, what would be the interpretation of the coefficient 55 in the function? a) The number of miles Laura has driven kingore the trip b)The rate at which Laura travels in miles per hour c)The total distance Laura travels in miles d)The time it takes for Laura to reach her destination

Question

11 Laura is taking a road trip to a destination that's 250 miles away. She decides to model her trip with the distance function  d(t)=55 t+10 to predict how far she'll have driven after  t hours. In this scenario, what would be the interpretation of the coefficient 55 in the function? a) The number of miles Laura has driven kingore the trip b)The rate at which Laura travels in miles per hour c)The total distance Laura travels in miles d)The time it takes for Laura to reach her destination

Bytelearn · Accepted Answer

Function Structure: The distance function given is d(t) = 55t + 10. This function predicts the distance Laura will have driven after t hours. To understand the coefficient 55, we need to look at the structure of the function.Linear Function Form: The function is linear, which means it has the form d(t) = mt + b, where m is the slope of the line, and b is the y-intercept. In the context of a distance function, the slope (m) represents the rate of change of distance with respect to time, which is the speed or velocity.Rate of Travel Interpretation: In Laura's function, the coefficient 55 is in the position of the slope (m). Therefore, the coefficient 55 represents the rate at which Laura travels, in miles per hour.Constant Term Meaning: The other parts of the function, such as the constant term 10, do not represent the rate of travel. The constant term would represent the initial value of the distance function at t=0, which could be interpreted as the number of miles Laura has driven before the trip starts.Total Distance Calculation: Since the coefficient 55 is multiplied by the time variable t, it cannot represent the total distance Laura travels in miles, as the total distance depends on the time traveled and would be the entire expression 55t + 10 evaluated at a specific t.Time Measurement Clarification: The coefficient 55 also cannot represent the time it takes for Laura to reach her destination, as it is a rate (miles per hour), not a time measurement.

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