Question

max puts a stopper in the bathtub and turns on the faucet at t = 0. after 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub. write an equation that relates the number of gallons, g, to the time, t minutes. equation: g = square t

Explanation:

Step1: Define linear model

We assume a linear relationship $g = mt + b$, where $m$ is the rate, $b$ is initial gallons.

Step2: Set up equations from given data

At $t=5$, $g=11$: $11 = 5m + b$
At $t=10$, $g=22$: $22 = 10m + b$

Step3: Solve for $m$

Subtract first equation from second:
$22 - 11 = (10m + b) - (5m + b)$
$11 = 5m$
$m = \frac{11}{5} = 2.2$

Step4: Solve for $b$

Substitute $m=2.2$ into $11 = 5m + b$:
$11 = 5\times2.2 + b$
$11 = 11 + b$
$b = 0$

Step5: Form final equation

Substitute $m=2.2$ and $b=0$ into $g=mt+b$.

Answer:

$g = 2.2t$ (or $g = \frac{11}{5}t$)