Answer: 34.78 gallon
Step-by-step explanation:
Exponential equation for decay:
[tex]A=P(1-r)^t[/tex] , where p = initial amount, r= rate of decay , t= taime
As per given,
r= 8% = 0.08
For days 1 , i.e. at t= 0 , P= 32 gallons
[tex]1=32(1-0.08)^t\\\\\Rightarrow\ \dfrac{1}{32}=(1-0.08)^t \\\\\Rightarrow\ \ln \left(\frac{1}{32}\right)=t\log (0.92)\\\\\Rightarrow\ t=-\frac{5\ln \left(2\right)}{\ln \left(0.92\right)}=41.5\approx42[/tex]
Total water = [tex]\dfrac{a(1-r^n)}{1-r}=\dfrac{32(1-0.08^{42})}{1-0.08}=34.782[/tex]
hence, the the total number of gallons of water that leaked from the tank = 34.78 gallon approx.
