The number of eggs that Farmer Jones has in his chicken coop will grow exponentially as Farmer Jones buys more chickens to increase production. The number of eggs Farmer Jones has in the coop can be modeled by the equation y = 3x beginning on Day 1, where x is given by x = 1, and y is the number of eggs currently in the coop. If the coop can support only 4,000 eggs, and Farmer Jones empties the coop every day, on which day will the chickens produce too many eggs for the coop to support?
A. Day 6
B. Day 7
C. Day 8
D. Day 9
Answer:C
The number of eggs that Farmer Jones has in his chicken coop will grow exponentially as Farmer Jones buys more chickens to increase production. The number of eggs Farmer Jones has in the coop can be modeled by the equation y = 3x beginning on Day 1, where x is given by x = 1, and y is the number of eggs currently in the coop. If the coop can support only 4,000 eggs, and Farmer Jones empties the coop every day, on which day will the chickens produce too many eggs for the coop to support?
A. Day 6 B. Day 7 C. Day 8 D. Day 9
Explanation: C The best way to deal with this question is to Plug in the Answers (PITA), starting with (A). If x = 6, then y = 36 = 729. This is less than 4,000, so eliminate (A) and move to the next answer choice. If x = 7, then y = 37 = 2,187. This is still less than 4,000, so eliminate (B). If x = 8, then y = 38 = 6,561. This is greater than 4,000, so (C) must be the correct answer.