Question

We-Haul rents a moving truck for $30.00 and $0.50 per mile. You-Haut rents the same size moving truck for $1.00 per mile but with no upfront charge.

What is the rate of change for We-Haul?

A) $0.50 per mile
B) $1.00 per mile
C) $0.30 per mile
D) $30.50 per mile

Answer 1

The rate of change for We-Haul is option A) $0.50 per mile.

Step-by-step explanation:

The rate of change represents how one variable changes concerning another. In this scenario, the cost for renting a moving truck from We-Haul includes an upfront charge of $30.00 plus $0.50 per mile. The rate of change, or the cost increase per mile, is given by the coefficient of the variable (mile) in the cost function.

The cost function for We-Haul is represented as
`\( C_w = 30 + 0.50 \cdot m \)`, where
`\( C_w \)` is the total cost and m is the number of miles. Comparing this to the standard linear equation y = mx + b, where m is the slope (rate of change) and b is the y-intercept (upfront charge), we can see that the rate of change for We-Haul is $0.50 per mile.

On the other hand, You-Haut charges $1.00 per mile with no upfront charge. Therefore, the rate of change for You-Haut is simply $1.00 per mile. By understanding the cost structures of both companies, one can make an informed decision based on their specific moving needs, considering the trade-off between upfront charges and per-mile rates.