Answer :

Final answer:

The question is about the cost impact on the federal government when vehicles with different weights per axle, such as a semi-trailer and a Honda Fit, travel on freeways. The semi-trailer's weight per axle is 13 times that of the Honda Fit, and since the cost increases with the fourth power of weight, the cost for the semi-trailer is 28,561 times higher.

Explanation:

The question asks about the relationship between the weight per axle of two different vehicles and the corresponding cost inflicted on the federal government for their travel on an interstate freeway. To analyze this, we use the provided information which states that the weight per axle (w) is approximately 13 times greater for a semi-trailer when compared to a Honda Fit. If the cost to the federal government for wear and tear on the interstate is determined by the axle weight, then this cost can be said to increase by a power of four as the axle weight increases, since the relationship between axle weight and road wear is not linear but exponential.

Thus, if we represent the cost as C = k · w^4, where k is a constant, and we know that the semi-trailer's axle weight is 13 times that of the Honda Fit, then the increased cost that the semi-trailer imposes when it travels the same distance on the interstate freeway is 13^4 times greater. This is because (13w)^4 / (w^4) simplifies to 13^4, which equals 28,561 times greater, considering w is the weight per axle for the Honda Fit and 13w for the semi-trailer.

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