Respuesta :
Answer:
Monthly growth function is [tex]i(x)=12 \times (1+\frac{0.9}{12})^{12x}[/tex] and growth rate is 0.075.
Step-by-step explanation:
We are given,
The function which models the population of iguanas in a reptile garden is [tex]i(x)=12 \times 1.9^{x}[/tex], where x is the number of years.
As, [tex]i(x)=12 \times 1.9^{x}[/tex]
i.e. [tex]i(x)=12 \times (1+0.9)^{x}[/tex]
So, the monthly growth rate function becomes,
[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 population of iguanas is i.e. [tex]i(x)=12 \times (1+\frac{0.9}{12})^{12x}[/tex].
Moreover, the growth factor is [tex]\frac{0.9}{12}[/tex] = 0.075.
Hence, the growth factor rounded to nearest thousandth is 0.075
