In a city with a population of 1,200,000, there are currently 1000 cases of infection with the HIV virus. If the spread of the disease is projected by the formula $$p = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 t } }$$ how many people will be infected in 6 years?
A)5,300 people
B)11,000 people
C)302,100 people
D)10,900 people
E)60,800 people

Question

Quizplus · Accepted Answer

To find the number of people infected in 6 years, substitute $t = 6$ into the given formula: $$p = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 \times 6 } }$$ Simplifying this gives the number of people infected after 6 years, which is closest to the number given in option D, 10,900 people.

In a City with a Population of 1,200,000, There Are p=1,200,0001+(1200−1)e−0.4tp = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 t } }p=1+(1200−1)e−0.4t1,200,000​

In a City with a Population of 1,200,000, There Are $p = \frac { 1,200,000 } { 1 + ( 1200 - 1 ) e ^ { - 0.4 t } }$