Answer: No, his prediction is unreasonable. After 5 minutes, the number of cells would be 400, not 32. See the explanation below for details.
-------
Remember:
- [tex]a_{n}[/tex] = [tex]n[/tex]th term
- [tex]n[/tex] = number of terms
- [tex]a_{1}[/tex] = first term
- [tex]r[/tex] = common ratio
-------
Identify the given information.
[tex]a_{1}[/tex] = 25
[tex]r[/tex] = 2
Use the explicit formula for geometric sequences.
[tex]a_{n} = a_{1} r^{n - 1}[/tex]
Substitute the given values.
[tex]a_{n} = (25)(2)^{n - 1}[/tex]
Substitute in 5 for [tex]n[/tex] to find out how many cells there would be after 5 minutes.
[tex]a_{5} = (25)(2)^{5 - 1} \\\\a_{5} = (25)(2)^{4} \\\\a_{5} = (25)(16)\\\\a_{5} = 400[/tex]
