Question on percentages(Pollution in the atmosphere)

Question

What I tried:

$$20*(1-\frac{80}{100})^n=0.01$$ $$=>(\frac{2}{10})^n=\frac{1}{2000}$$

But by this n is not having any integer value!

Answer 1

We can write this as a logarithm, which can be converted into $\log_{2/10} \frac{1}{2000} = n$. By the change of base formula, we have $n = \frac{ \ln{1/2000} } {\ln{2/10} }$, which equals approximately $4.723$.

Now, the question asks you "how many days will the pollution return to normal levels". Notice it takes around $4.723$ days for the pollution to reach its normal level exactly. Will the pollution be cleaned up in $4$ days? How about in $5$ days?