Answer:
7680 bats
Step-by-step explanation:
The number of bats in a colony is growing exponentially.
The formula for exponential growth =
y = ab^t
Where t = time in years
From the above question, we are told that:
After 2 years, there were 120 bats. After 5 years, there were 960 bats.
So we form an equation
120 = ab²...... Equation 1
960 = ab⁵ ....... Equation 2
Hence:
120/960 = ab²/ab⁵
1/8 = b²/b⁵
1/8 = 1/ b^5 - 2
1/8 = 1/b³
1/2³ =1/ b³
2^-3 = b^-3
b = 2
We solve for a
120 = ab²...... Equation 1
120 = a × 2²
120 = 4a
a = 120/4
a = 30
If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 8 years?
Using the formula
y = ab^t
t = 8
a = 30, b = 2
y = 30 × 2⁸
y = 7680 bats
