Question

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.

Answer 1

23040 bats

Step-by-step 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