The number of bats in a colony is growing exponentially. After 2 years, there were 180 bats. After 5 years, there were 1440 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 9 years? Do not include units in your 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