Question

On a small volcanic island, lava is flowing at a rate of 800 meters per day and can be modeled by the function f(d) = 800d, where f(d) represents the distance from the source of the lava flow, and d represents the day of the flow.

The domain of f(d) in this context is best described as ____ .

Answer 1

We want to find the domain for the given function.

We will get that the domain is continuous and is something like:

D: [0, ∞)

We have the function:

f(d) = 800*d

Where d represents the day of the flow and f is the distance from the source of the lava flow.

We want to find the domain of this function, remember that the domain is the set of inputs that we can use on the function. In this case, is the number of days.

So knowing that the lava flows at a constant rate (is not like for the whole day 1 it advanced 800 meters, and as soon as day 2 arrives it moves another 800 meters) then we can assume that the domain is continuous.

This means that f(1.5) would represent the distance from the source after one day and a half.

We also can try to find an interval where the domain lies.

The minimum of the domain is d = 0, we can't have negative values for the domain as those do not make sense in the situation.

Sadly, we can't get a maximum for the domain (we don't know when the lava will stop flowing) then we can say that the domain is something like:

D: [0, ∞)

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