Question

A fish aquarium is leaking a a rate of 1 quarter per minute. The aquarium started out with 200 gallons. Write a linear model showing how much water is left in gallons after m minutes

Answer 1

Answer:

Linear model: $V=-\frac{1}{4}m+200$

Step-by-step explanation:

Let the volume of water left after $m$ minutes be $V$ gallons.

Let the leakage rate be $R$ gallons per minute.

From the question,

Rate of leakage is given as 1 quarter per minute.

1 quarter is $\frac{1}{4}$ of a gallon. So,

$R=-\frac{1}{4}$ gallons per minute. Negative sign is used since the volume is decreasing per minute.

Now, initial volume is 200 gallons.

So, a linear model will be of the form:

$V=-\frac{1}{4}m+200$

The above equation represents volume of water left in gallons after $m$ minutes.