Answer:
There will be 88.6% of her bone mass remaining when she returns to earth.
Step-by-step explanation:
According to the problem, the astronaut will have 2% less bone mass than at the beginning of that month. So let's say [tex]B_{0}[/tex] is her original bone mass. In that case, her bone mass after the first month will be:
[tex]B_{1}=B_{0}(0.98)[/tex]
on the second month, her bone mass will be:
[tex]B_{2}=B_{1}(0.98)=B_{0}(0.98)(0.98)=B_{0}(0.98)^{2}[/tex]
on the third month, her bone mass will be:
[tex]B_{3}=B_{2}(0.98)=B_{0}(0.98)(0.98)(098)=B_{0}(0.98)^{3}[/tex]
and so on, we can see a pattern here. The formula for her remaining bone mass can be generally written like this:
[tex]B_{n}=B_{0}(0.98)^{n}[/tex]
where n is the number of months, so after 6 months, her remaining bone mass will be:
[tex]B_{6}=B_{0}(0.98)^{6}=0.886B_{0}[/tex]
that 0.886 gives us the percentage as a decimal number. When turned into a percentage we get that:
There will be 88.6% of her bone mass remaining after 6 months.
