Question

The level of a lake in inches is falling linearly . The lake level is 452 inches on Jan 1 and then 378 inches on Jan 21. Find a function to represent the lake level

Answer 1

`y=-(74)/(21)x+452`

Explanation:

Given:

The level of a lake is falling linearly.

On Jan 1, the level is 452 inches

On Jan 21, the level is 378 inches.

Now, a linear function can be represented in the form:

`y=mx+b`

Where, 'm' is the rate of change and 'b' is initial level

`x\to number\ of\ days\ passed\ since\ Jan\ 1`

`y\to Lake\ level`

So, let Jan 1 corresponds to the initial level and thus b = 452 in

Now, the rate of change is given as the ratio of the change in level of lake to the number of days passed.

So, from Jan 1 to Jan 21, the days passed is 21.

Change in level = Level on Jan 21 - Level on Jan 1

Change in level = 378 in - 452 in = -74 in

Now, rate of change is given as:

`m=(-74)/(21)`

Hence, the function to represent the lake level is
`y=-(74)/(21)x+452`

Where, 'x' is the number of days passed since Jan 1.