Anna should use the following equation,
[tex]a_{15} = 4(3)^{15}[/tex]
Equation for Determining the Number of Bacterial Cells
Initially, the count of bacterial cells = 4
It is given that the bacterial cell triples every month.
Hence, the equation for the count of bacterial cells after first month is,
a₁ = 4(3)
This count of 4(3) triples again in the second month.
So, after the second month, the equation for the count of bacterial cells is given by,
a₂ = 4(3)(3) = 4(3)²
Calculating the Count of Bacterial Cells For Each Month
Again, this count triples in the third month.
Therefore, the equation for the count of bacterial cells after the third month becomes,
a₃ = 4(3)(3)(3) = 4(3)³
This count triples again in the fourth month and this process continues till 15 months.
Hence, the equation for determining the number of bacterial cells comes out to be as follows,
a₁₅ = 4(3)¹⁵
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