Question

If the current population size of bison is $3652$ and the maximum growth rate of the population is $0.28$, calculate the population size after one year and determine whether the park will need to take measures to control the population.

Answer 1

Explanation

Given,

Present population of bison ${\mathrm{P}}_{\mathrm{F}}$ $=3652$

Maximum growth rate $\mathrm{r}$$=0.28$

Time $\mathrm{n}$ = $1\mathrm{year}$

The future population can be calculated with the help of the following formula,

${\mathrm{P}}_{\mathrm{F}}={\mathrm{P}}_{\mathrm{P}}\times {(1+\mathrm{r})}^{\mathrm{n}}$

where, ${\mathrm{P}}_{\mathrm{F}}$ is the future population, ${\mathrm{P}}_{\mathrm{P}}$ is the present population, $\mathrm{r}$ is the growth rate and $\mathrm{n}$ is the number of years.

On substituting the given values in the formula we get,

$$\begin{gathered} \Rightarrow {\mathrm{P}}_{\mathrm{F}}=3652\times {(1+0.28)}^1 \\ \Rightarrow {\mathrm{P}}_{\mathrm{F}}=3652\times 1.28=4674.56\approx 4675 \end{gathered}$$

Therefore, the population size of bison after one year is $4675$.

The park does not have to control the population because the growth rate is on an average scale.