After 11 years the expected bats in the colony = 4074381 bats.
An exponential function exists as a mathematical function of the subsequent form: [tex]f ( x ) = a ^{x}[/tex].
where x exists a variable, and a exists a constant named the base of the function. The most generally encountered exponential-function base exists the transcendental number e, which exists equivalent to approximately 2.71828.
Let N(t) be the number of bats at time t
We know that exponential function
[tex]y = ab^2[/tex]
According to question
[tex]N(t) = ab^2[/tex]
Where t (in years)
Substitute t = 2 and N(2) = 207
[tex]207 = ab^2[/tex] ...(1)
Substitute t = 4 and N(4) = 1863
[tex]1863 = ab^2[/tex] ...(2)
Equation (1) divided by equation (2)
207/1863 = [tex]ab^2/ab^2[/tex]
[tex]$= 1/b^{4-2}[/tex]
By using the property
[tex]a^x/a^y = a^{x-y}[/tex]
[tex]a^2/a^4 = a^{4-2}[/tex]
1/9 = [tex]1/b^2[/tex]
[tex]b^2 = 9 =3*3 = 3^2[/tex]
b = 3
Substitute the values of b in (1)
207 = [tex]a(3)^2[/tex] = 9a
a = 207/9 = 23
Substitute t = 11
N(11) = [tex]23(3)^{11}[/tex]= 4074381 bats
Hence, after 11 years the expected bats in the colony = 4074381 bats.
To learn more about exponential function refer to:
https://brainly.com/question/14804974
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