Question

Carlos is on a highway that passes through Mitchell, South Dakota. He travels at 75

miles per hour, starting 150 miles from Mitchell and continues past it. Write a function that represents Carlos' distance, , from Mitchell based on the number of hours, , since he started. What is the domain for ?


Please answer the question and provide some explanation :) thanks

Answer 1

Explanation:

To represent Carlos' distance from Mitchell based on the number of hours since he started, we can use the formula:

distance = initial distance + (speed * time)

In this case, Carlos starts 150 miles from Mitchell and travels at a speed of 75 miles per hour. Let's use the variable "d" to represent the distance from Mitchell and "t" to represent the number of hours since Carlos started.

So, the function that represents Carlos' distance from Mitchell is:

d(t) = 150 + (75 * t)

Now, let's determine the domain for the function. The domain represents all the valid inputs for the function, in this case, the number of hours since Carlos started.

In this situation, Carlos continues past Mitchell, so the function should represent all positive values of time since he started. Therefore, the domain for the function is all real numbers greater than or equal to zero (t ≥ 0).

To summarize, the function representing Carlos' distance from Mitchell is d(t) = 150 + (75 * t), and the domain for the function is t ≥ 0, which means all non-negative real numbers.