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Derek found a function that approximately models the population of iguanas in a reptile garden, where x represents the number of years since the iguanas were introduced into the garden.


i(x) = 12(1.9)^x


Rewrite this function in a form that reveals the monthly growth rate of the population of iguanas in the garden. Round the growth factor to the nearest thousandth.

Respuesta :

Answer:

[tex]i(x)=12 \times (1+\frac{0.9}{12})^{12x}[/tex] and growth rate factor is 0.075

Step-by-step explanation:

The function that models the population of iguanas in a reptile garden is given by [tex]i(x)=12 \times (1.9)^{x}[/tex], where x is the number of years.

Since, [tex]i(x)=12 \times (1.9)^{x}[/tex]

i.e. [tex]i(x)=12 \times (1+0.9)^{x}[/tex].

Therefore, the monthly growth rate function becomes,

i.e. [tex]i(x)=12 \times (1+\frac{0.9}{12})^{x \times 12}[/tex].

i.e. [tex]i(x)=12 \times (1+\frac{0.9}{12})^{12x}[/tex].

Hence, the monthly growth rate is i.e. [tex]i(x)=12 \times (1+\frac{0.9}{12})^{12x}[/tex].

Also, the growth factor is given by [tex]\frac{0.9}{12}[/tex] = 0.075.

Thus, the growth factor to nearest thousandth place is 0.075.

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