Answer:
the population be on Week 20 is about 665,051
Step-by-step explanation:
The growth of a bug population shows a geometric sequence as shown in the table
For all geometric sequence , there should be a common ratio
Lets find common ratio 'r'
To find common ratio we divide second term by first term
so common ratio [tex]r= \frac{450}{300} =\frac{3}{2}[/tex]
To find nth term of geometric sequence , formula is
[tex]a_n = a_1(r)^{n-1}[/tex]
Where a1 is the first term and r is the common difference
a1= 300 and r= 3/2
We need to find the population on Week 20, so n= 20
We plug in all the values and find out a20
[tex]a_{20} = 300(\frac{3}{2})^{20-1}[/tex]
[tex]a_{20} = 300(\frac{3}{2})^{19}=300*2216.83782=665051.346[/tex]
the population be on Week 20 is about 665,051
