Question

What is the explicit formula for the growth rate f bacteria spores

Answer 1

From the table given, Using the bacteria spores column,

a is the first term, r is the common ratio

We can deduce our first term, a is 2

The second term is 4 and the third term is 8 and n represents the number of terms,

Obviously, the sequence is not arithmetic but a geometric progression.

`\begin{gathered} \text{first term, a=2} \\ \text{second term is 4} \\ \text{common ratio, r=}\frac{2^(nd)\text{ term}}{1^(st)\text{ term}}=(4)/(2)=2 \\ r=2 \end{gathered}`

Hence r = 2

Using the formula for a geometric progression,

`U_n=ar^(n-1)`
`\begin{gathered} \text{Where a=2 and r=2} \\ \text{Substitute the values of a and r into the above geometric formula} \\ U_n=2(2)^(n-1) \end{gathered}`

Hence, the explicit formula has been deduced above.