Answer:
23040 bats
Explanation:
Let N(t) be the number of bats at time t
We know that exponential function
y = ab^t
According to question
N(t) = ab^t
Where t (in years)
Substitute t=2 and N(2)=180
180 =ab^t ...(1)
Substitute t=5 and N(5)=1440
1440 = ab^5. ..........(2)
Equation (1) divided by equation (2)
180/1440 = ab^2 ÷ ab^5
1/8 = 1/b^3
8 = 2^3
Hence,
1/2^3 = 1/b^3
3/2 = 3/b
Cross multiply
3b = 2×3
3b =6
b = 2
Substitute the values of b in equation (1)
180 = a(2)^2
180 = 4a
a = 180/4
a = 45
Substitute t=9
N(9) = 45(2)^9
N = 45 × 512
N =23040
Hence, after 9 years the expected bats in the colony=23040 bats
