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Answer :
Final answer:
The correct model for the population growth of the frogs, which increases by 14% annually from an initial population of 57, is 57(1.14)^t, where 't' is the number of years.
Explanation:
The population of a certain species of frog grows 14% every year, and we're starting with 57 frogs. To model this population growth, we need an equation that includes the initial number of frogs and accounts for the 14% annual increase. The correct model would be c. 57(1.14)^t, where 't' represents the number of years since the frogs were released. This model multiplies the initial population by 1.14 (which represents a 14% increase) every year.
The other options are incorrect because option a doesn't account for compounding growth over multiple years, option b is not a meaningful expression for population growth, and option d is incorrect because it raises 1.14 to the 57th power, which has no relation to the concept of annual population growth.
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