Question

A hole is accidentally made in a water tank. On the first day, 32 gallons of water leak from the tank. Each day after that, workers are able to decrease the number of gallons leaking by 8% of the leakage on the day before. What is the total number of gallons of water that leaked from the tank?

Answer 1

Answer: 34.78 gallon

Explanation:

Exponential equation for decay:

`A=P(1-r)^t` , 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

`1=32(1-0.08)^t\\\\\Rightarrow\ (1)/(32)=(1-0.08)^t \\\\\Rightarrow\ \ln \left((1)/(32)\right)=t\log (0.92)\\\\\Rightarrow\ t=-(5\ln \left(2\right))/(\ln \left(0.92\right))=41.5\approx42`

Total water =
`(a(1-r^n))/(1-r)=(32(1-0.08^(42)))/(1-0.08)=34.782`

hence, the the total number of gallons of water that leaked from the tank = 34.78 gallon approx.