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An intitial population of 745 quail increases at an annual rate of 16%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?

Respuesta :

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &745\\ r=rate\to 16\%\to \frac{16}{100}\to &0.16\\ t=\textit{elapsed time}\to &t\\ \end{cases} \\\\\\ A=745(1+0.16)^t[/tex]

and after 4 years?  well, t = 4, so    [tex]\bf A=745(1+0.16)^4[/tex]
Parrain

Based on the initial population of the quails and the rate at which they are increasing, the exponential function would be 745 x ( 1 + 16%) ^ n and the population after 4 years would be 1,348 quails.

The population of quail at any period of time is:

= Initial population x ( 1 + rate of increase) ^ number of years

Assuming number of years is n, the function would be:

= 745 x ( 1 + 16%) ^ n

If n is 4 years, the population would be:

= 745 x ( 1 + 16%)⁴

= 1,348 quails

In conclusion, the population would be 1,348 quails.

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