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He number of bats in a colony is growing exponentially. after 2 years, there were 220 bats. after 4 years, there were 880 bats. if the colony continues to grow at the same rate, how many bats are expected to be in the colony after 10 years? do not include units in your answer.

Respuesta :

sqdancefan

An exponential equation can be written from its description using the form

... y = (reference value)·((later value)/(reference value))^((t - (reference time))/(later time - reference time))

Here, we have

... reference value = 220; reference time = 2; later value = 880; later time = 4

so we can write the exponential equation as

... y = 220·(880/220)^((t-2)/(4-2)) = 220·4^(t/2 -1) = 55·2^t

Then for t=10, the expected number is

... y = 55·2^10 = 56,320