Under ideal conditions, Lemna minor (common duckweed) is a fastgrowing fern that can double its area every 2 days. Assume the growth is unrestricted, and that the duckweed initially covers 10 square centimeters (cm^(2)) in area. Which of the following functions, F, models the area (in cm^(2) ) the duckweed covers after d days? Choose 1 answer: (A) F(d)=10(0.5)^((d)/(2)) (B) F(d)=2(10)^(d) (c) F(d)=10(2)^(d) (D) F(d)=10(2)^((d)/(2))

Question

Under ideal conditions, Lemna minor (common duckweed) is a fastgrowing fern that can double its area every 2 days. Assume the growth is unrestricted, and that the duckweed initially covers 10 square centimeters  (cm^(2)) in area. Which of the following functions,  F, models the area (in  cm^(2) ) the duckweed covers after  d days? Choose 1 answer: (A)  F(d)=10(0.5)^((d)/(2)) (B)  F(d)=2(10)^(d) (c)  F(d)=10(2)^(d) (D)  F(d)=10(2)^((d)/(2))

Bytelearn · Accepted Answer

Problem Understanding: Understand the problem. We need to find a function that models the growth of the duckweed, which doubles in area every 2 days, starting from an initial area of 10 cm^2.Analyzing Answer Choices: Analyze the answer choices. (A) F(d)=10(0.5)^(d/2) suggests the area is halved every 2 days, which is the opposite of what we want. (B) F(d)=2(10)^d suggests the area is multiplied by 10 raised to the power of the number of days, which is not a doubling every 2 days. (C) F(d)=10(2)^d suggests the area doubles every day, which is faster than the given rate. (D) F(d)=10(2)^(d/2) suggests the area is multiplied by 2 raised to the power of half the number of days, which could represent a doubling every 2 days.Determining the Correct Model: Determine the correct model by testing the doubling condition. We know that after 2 days, the area should be double the initial area, which is 20 cm^2. Let's test option (D) since it seems to fit the doubling condition: F(2) = 10(2)^(2/2) = 10(2)^1 = 10 * 2 = 20 cm^2. This matches the condition that the duckweed doubles its area every 2 days.Confirming Other Options: Confirm that the other options do not match the doubling condition. (A) F(2) = 10(0.5)^(2/2) = 10(0.5)^1 = 10 * 0.5 = 5 cm^2, which is incorrect. (B) F(2) = 2(10)^2 is clearly much larger than 20 cm^2, which is incorrect. (C) F(2) = 10(2)^2 = 10 * 4 = 40 cm^2, which is also incorrect.Concluding the Correct Function: Conclude the correct function. Based on the analysis, the function that correctly models the growth of the duckweed is (D) F(d)=10(2)^(d/2).

Full solution

More problems from Compare linear and exponential growth

Related topics