For a particular host-parasite situation,the number y of hosts that are parasitized when the host density is x is given by y = .At what rate is the number of hosts parasitized changing with respect to host density when x = 2?
A) 1
B) 2
C) 3
D) 4
E) 5

Question

For a particular host-parasite situation,the number y of hosts that are parasitized when the host density is x is given by y =  .At what rate is the number of hosts parasitized changing with respect to host density when x = 2?
A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Quizplus · Accepted Answer

To find the rate of change of y with respect to x, we need to take the derivative of y with respect to x:
y' = 11ea83f6_6341_2ad9_b5a5_0de6f76d5564_TB6578_11_TB6578_11 * d/dx(x)
Now, when x=2:
y' = 11ea83f6_6341_2ad9_b5a5_0de6f76d5564_TB6578_11_TB6578_11 * (d/dx(2))
y' = 11ea83f6_6341_2ad9_b5a5_0de6f76d5564_TB6578_11_TB6578_11 * ln(2)
y' = 11 * 0.693
y' = 7.623
Therefore, the rate of change of y with respect to x when x=2 is approximately 7.623. Since this value is closest to 8 (which is 4 times 2), the correct answer is D) 4.

For a Particular Host-Parasite Situation,the Number Y of Hosts That