the number of cells in a sample doubles every minute. A doctor with a sample of 25 cells and predicted that, after 5 minutes, he would have 32 cells. Is his prediction reasonable? Explained
Accepted Solution
A:
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] = 2Use 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]