Answer:
23040 bats
Step-by-step explanation:
Let N(t) be the number of bats at time
We know that exponential function
[tex]y = ab[/tex]
According to question
[tex]N(t) = ab^{2}[/tex]
Where t (in years)
Substitute t=2 and N(2)=180
[tex]180 = ab^{2}[/tex]
Substitute t=5 and N(5)=1440
[tex]1440 = ab^{5}[/tex]
Equation (1) divided by equation (2)
[tex]\frac{180}{1440} = \frac{ab^{2} }{ab^{5}} = \frac{1}{b\frac{5-2}{}}[/tex]
By using the property
Substitute the values of b in equation (1)
Substitute t=9
Hence, after 9 years the expected bats in the colony=23040 bats
