The initial population size was 53 hippogriffs. After only 5 year(s), a new count was taken revealing 68 hippogriffs. Assuming the population of hippogriffs is best modeled with an exponential function, estimate the number of hippogriffs in the count taken after a total of 12 years.

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A: This question is related to speed, time and distance, we will solve it using given information.

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A: answer is in next step

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A: answer is in next step

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A: Let's find.

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A: Given problem:- Find two consecutive positive integers such that the sum of their squares is 265.

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A: I am attaching image so that you understand each and every step.

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A: answer is in next step