Answer:
a) [tex]a(t)=7e^{\frac{-t}{325} }[/tex]
b) it is noticeable
Step-by-step explanation:
a) Let a(t) be the amount of die at time t. a is in kg and t is in minutes. Therefore:
[tex]\frac{da}{dt} =\frac{-a(t)}{65000}*\frac{200gal}{1 min}=\frac{-a}{325}\\\frac{da}{a} =\frac{-1}{325} dt\\\int\limits{\frac{1}{a} } \, da =\int\limits{\frac{-1}{325} } \, dt\\ln(a)=\frac{-1}{325} t+c\\a=ce^{\frac{-t}{325} }\\at\ t=0, a=7\\ 7=ce^0\\c=7\\a(t)=7e^{\frac{-t}{325} }[/tex]
b) 4 hrs = (4 * 60) min = 240 min
[tex]a(t)=7e^{\frac{-t}{325} }\\a(240)=7e^\frac{-240}{325} = 3.345kg[/tex]
3.345 kg = (3.345 * 1000 / 60000) g/gal = 0.0557 g/gal
0.0557 g/gal > 0.03 g/gal, therefore it is noticeable
