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The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2010 was 23,900. Find a function for the population and estimate the fox population in the year 2018.

Respuesta :

opudodennis

Answer:

49101

Step-by-step explanation:

-We notice that this is an exponential growth problem.

-Exponential growth is expressed as:

[tex]A_t=A_oe^{kt},\\\\A_t-pop \ at\ t\\A_o-Intial \ pop\\k-growth \ constant\\t-time[/tex]

Let X be the initial population growing at 9%, Given the initial time as 2010 and the final time as 2018, our population is estimated as:

[tex]A_t=23900^{(2018-2010)K}\\\\=23900e^{8\times 0.09}\\\\=49100.95\approx49101[/tex]

Hence, the fox population is estimated to be 49,101 in 2018

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