The number of bats in a colony is growing exponentially. After 2 years, there were 120 bats. After 5 years, there were 960 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 8 years?

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

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step-by-step explanation: