A half-life is the time taken for the radioactivity of a specified isotope to fall to half its original value. If an isotope had 40g after 2 half-lives the isotope would be reduced to just 10g. 40\cdot\frac{1}{2}\cdot\frac{1}{2}= 1040⋅

2

1



⋅

2

1



=10

Using the function f\left(x\right)=100\cdot\left(\frac {1}{2}\right)^xf(x)=100⋅(

2

1



)

x

where 100 is the original value of the isotope and x is the number of days that have happened.

What is the first day that an isotope with 100g falls below 1g?