There were 218 loggerhead sea turtle nests on a certain beach in 2017. Environmentalists are working to protect the turtles, and they predict that the number of nests on the beach each year after 2017 will be 1.5 percent greater than the number of nests on the beach in the preceding year. According to the prediction, which of the following represents the number of loggerhead sea turtle nests that will be on the beach in 2020?

Rationale

218(1.015)^3

The number of loggerhead sea turtle nests in 2020 can be calculated using the formula for compound growth, where the initial number of nests (218) is multiplied by the growth factor (1.015) raised to the power of the number of years (3) since 2017.

A (218(1.015)^3) CORRECT

This choice accurately represents the growth of the number of nests over three years, where 1.015 corresponds to a 1.5% increase (1 + 0.015) each year, compounded annually. This formula correctly calculates the predicted number of nests for 2020, following the environmentalists' projection.

B (218(1.5)^3) YOUR ANSWER

This option incorrectly uses 1.5 as the growth factor. Instead, it should use 1.015 to reflect a 1.5% increase. Using 1.5 would imply a 50% growth rate, which is not aligned with the given prediction of a 1.5% increase each year.

C ((218 + 0.015) ^ 3) YOUR ANSWER

This choice erroneously suggests adding 0.015 directly to 218 and then cubing the result. This does not accurately represent annual growth since it ignores the compounding effect of the percentage increase over multiple years.

D (218+3(1.015)) YOUR ANSWER

This option incorrectly represents the calculation by applying a linear growth model rather than a compound growth model. It implies a simple addition of the growth for each year rather than compounding the growth, which underestimates the actual number of nests.

E (218+3(1.5)) YOUR ANSWER

Similar to option D, this choice assumes a linear increase rather than a compounded one. It adds a total of 4.5 (3 times 1.5) to the initial count, misrepresenting the growth mechanism and leading to an inaccurate prediction.

Conclusion

The correct approach to predict the number of loggerhead sea turtle nests in 2020 is to use the compound growth formula, represented by 218(1.015)^3. This method accurately reflects the 1.5% annual increase compounded over three years, ensuring that the calculation aligns with the environmentalists' projection. Other options fail to utilize the correct growth model, leading to inaccurate results.

218(1.015)^3

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test