The function that models the number of years, f(n) , it will take the population to reach a size of n individuals :- [tex]f(n)=1800\times (0.84)^n[/tex]
"It defines a relation between input and output values."
"It is a number can be expressed as a fraction of 100."
"[tex]y=a(1-r)^t[/tex] where a is the initial value,
r is the rate of decay,
and t is the time period."
For given question,
The current population size is 1,800
So, a = 1800
The population is decreasing by 16% per year.
We can write above percentage as,
[tex]16\%\\=\frac{16}{100}\\\\ =0.16[/tex]
So, the decay rate (r) = 0.047
We need to find the function that models the number of years, f(n) , it will take the population to reach a size of n individuals.
Using exponential decay formula,
[tex]\Rightarrow f(n)=1800\times(1-0.16)^n\\\\\Rightarrow f(n)=1800\times (0.84)^n[/tex]
Therefore, the function that models the number of years, f(n) , it will take the population to reach a size of n individuals :- [tex]f(n)=1800\times (0.84)^n[/tex]
Learn more about the exponential decay here:
brainly.com/question/14355665
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