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The number of bats in a colony is growing exponentially. After 3 years, there were 272 bats. After 5 years, there were 1088 bats.

If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.

Respuesta :

adioabiola

The number of bats are expected to be in the colony after 11 years if the colony continues to grow at the same rate is 69,632

Exponential function

Let

  • Number of bat at a time = n(t)

exponential function;

y = ax^t

When t = 3

272 = ax³

when t = 5

1088 = ax^5

  • divide both equation

272/1088 = ax^3 / ax^5

1/4 = x^3-5

1/4 = x^-3

1/4 = 1/x²

1 × x² = 4 × 1

x² = 4

x = 2

Substitute x = 2 into

272 = ax³

272 = a × 2³

272 = a × 8

272 = 8a

a = 272/8

a = 34

Number of bat expected at the colony after 11 years

y = ax^t

= 34 × 2^11

= 34 × 2048

y = 69,632 bats

Learn more about exponential function:

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