If a rancher has one sheep with hoof and mouth disease in a flock of 1600, then the time in days t for n sheep to become infected is modeled by . To the nearest tenth, find the number of days it takes for one-half of the flock to contract the disease.
A) 14.8 days
B) 22.1 days
C) 15.6 days
D) 36.8 days

Question

If a rancher has one sheep with hoof and mouth disease in a flock of 1600, then the time in days t for n sheep to become infected is modeled by  . To the nearest tenth, find the number of days it takes for one-half of the flock to contract the disease.
A) 14.8 days 
B) 22.1 days 
C) 15.6 days 
D) 36.8 days

Quizplus · Accepted Answer

The equation given is t = (-1/1600)ln(1- n/1600)/(1/10). 
To find the number of days it takes for half of the flock to contract the disease, we substitute n = 800 into the equation:

t = (-1/1600)ln(1- 800/1600)/(1/10) ≈ 22.1 days (rounded to the nearest tenth)

Therefore, the best choice is B.

If a Rancher Has One Sheep with Hoof and Mouth