Question

Write a linear function that represents the depth of the pond at a given time

Answer 1

Let x represent the number of days

Let f(x) represent water depth

We can see that the water depth is a function of the number of days.

Water depth, f(x) is the dependent variable and number of days, x is the independent variable.

As the days go by, the water depth changes.

The function is therefore:

`f(x)=54-0.5x`

The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.

`0\le x\le108`

Because at 0 days,

`f(x)=54-0.5(0)=54^(\doubleprime)`

And at 108 days,

`f\mleft(x\mright)=54-0.5\mleft(108\mright)=0`