Question

Here we are again because i don't understand a bit.

Answer 1

We have a function with an exponetial form:

`\begin{gathered} f(t)=a\cdot b^t \\ In\text{ this case:} \\ f(t)=54\cdot2.718^(0.12t) \\ \text{Where t is the time in month} \end{gathered}`

The initial value is when t=0 (means 0 month), so:

`\begin{gathered} f(t=0)=a\cdot b^0=a,b^0=1\text{ for any b} \\ f(t=0)=54\cdot2.718^(0.12\cdot0)=54 \end{gathered}`

When the researcher started the number of birds was 54. This discard the second and the last option.

And, we can find the concept of b taking the ratio of f(t) for two different values of t:

`\begin{gathered} We\text{ say:} \\ t_2>t_1\ge0 \\ f(t_2)=a\cdot b^(t_2) \\ f(t_1)=a\cdot b^(t_1) \\ \frac{f(t_2)_{}}{f(t_1)}=(a\cdot b^(t_2))/(a\cdot b^(t_1))=b^((t_2-t_1)),t_2-t_1>0 \end{gathered}`

So, the base b is related with the growth of the population, if b is greater than 1 the population increase with time, if b is less than 1 the population decrease with time.

So, the correct answer is the first option.