Given the following question:
Stacy is 100% certain she will meet Lady Gaga
For every year she doesn't meet Lady Gaga she is half as certain that it will happen.
Let d(t) = certainly that Stacy's dream comes true
Let t = the number of years
[tex]d(t)=100\times(\frac{1}{2})^t[/tex]
You can check your work by testing the function, substitute a number in for t to represent the years.
[tex]\begin{gathered} t=2 \\ d(t)=100\times(\frac{1}{2})^2 \\ \frac{1}{2}^2=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ d(t)=100\times\frac{1}{4} \\ 100\times\frac{1}{4}=\frac{100}{4}=100\div4=25 \\ =\text{ Stacy is}25\text{ percent certain she will see lady gaga} \end{gathered}[/tex]
