33. 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?
Answer: A
The number of loggerhead sea turtle nests that will be on the beach in 2020 is represented by 218(1.015)^3.
To find the predicted number of loggerhead sea turtle nests in 2020, we apply a 1.5 percent growth rate to the initial 218 nests for each of the three years after 2017. This is accurately expressed by the formula 218(1.015)^3, where 1.015 accounts for the growth factor.
A) 218(1.015)^3
This option is correct as it correctly applies the formula for compound growth. The expression reflects the initial number of nests (218) multiplied by the growth factor (1.015) raised to the power of 3, which accounts for the increase over three years (2018, 2019, and 2020).
B) 218(1.5)^3
This option is incorrect because it misapplies the growth rate. The factor of 1.5 does not represent a percentage increase but rather a multiplicative increase of 50%, which is not the intended calculation for a 1.5% annual growth.
C) (218 + 0.015) ^ 3
This option is also incorrect as it suggests adding 0.015 directly to 218 and then cubing the result. This does not reflect the compounding growth mechanism and misrepresents how percentage increases work.
D) 218+3(1.015)
This option is incorrect because it inaccurately applies a linear growth approach rather than compounding the growth over three years. It suggests a simple addition of three times the growth rate, which does not reflect the correct prediction for the nests.
E) 218+3(1.5)
This option is incorrect as it uses a linear growth assumption with an incorrect growth rate. It suggests adding a total of 4.5 (3 times 1.5) to 218, which does not account for the percentage increase in the correct manner.
Conclusion
The correct answer, 218(1.015)^3, accurately reflects the predicted growth of the loggerhead sea turtle nests using the proper compounding formula for a 1.5 percent increase each year. All other options fail to use the correct mathematical approach to predict the number of nests, either by misapplying the growth rate or by using linear growth instead of exponential growth.