Question

A river in one part of the Rocky Mountains has a flow rate of 250 cubic meters of water per second. The flow of the water can be modeled mathematically with the function, w(t)=250t , where w (t) represents the volume of the water in cubic meters, at time t, in seconds. What does w(t)=7500 mean in this situation?

1250 m³
75000 m³
7500 m³
12500 m³

Answer 1

The equation w(t) = 7500 means that the river in the Rocky Mountains has flowed a volume of 7500 cubic meters of water after 30 seconds.

Step-by-step explanation:

The equation w(t) = 7500 represents the scenario where the river has flowed a volume of 7500 cubic meters of water. Since w(t) is the function that defines the volume based on time, we can see that to reach a volume of 7500 m³, we can replace w(t) with 7500 and solve for t. Given the function w(t) = 250t, we would set up the equation 7500 = 250t and solve for t to find the time necessary for the river to flow 7500 m³ of water.

To solve, divide both sides by 250, yielding t = 7500 / 250. This leads to t = 30 seconds. Therefore, w(t) = 7500 means that at time t = 30 seconds, the river has flowed a total of 7500 cubic meters of water.