Question

A barrel contains 149 gallons of water and is being drained at a constant rate of 15 gallons per hour. Write the equation that modles the number of gallons,g, after t hours.

Answer 1

how to get the equation\?

Answer 2

why g?

Answer 3

for gallons?

Answer 4

initial condition \[g(0)=g_0=149\left[ {\text{gallons of}\text{ H}_2\text O} \right]\]
rate of change
\[\frac{\text d g(t)}{\text dt}=-15 \left[\frac {\text{gallons}\text{ H}_2\text{O}}{\text {hour}}\right]\]\[\downarrow\]\[{\text d g(t)}=-15 \cdot\text dt\]\[{\int\text d g(t)}=\int-15 \cdot\text dt\]\[g(t)=-15\int\text dt\]

Answer 5

you'll be able to find the constant \(c\)
of integration by substituting
in \[g(0) \] at
\[t=0\]

Answer 6

@unkabogable !