Question

During an epidemic, the number of people who have never had the disease and who are not immune (they are susceptible) decreases exponentially according to the function f(x) = 15000e-^(0.05t) , where t is time in days. Find the number of susceptible people at each time below.

At the beginning of the epidemic

After 14 days

After 21 days

After 5 weeks

Answer 1

Solving this problem is just pretty straight forward. All we simply have to do is to plug in the value of t (in days) in the function, solve then we get the number of susceptible people.

 

A. At the beginning of the epidemic
t = 0

f(x) = 15000 e-^(0.05 * 0)

f(x) = 15000

 

B. After 14 days

t= 14

f(x) = 15000 e-^(0.05 * 14)

f(x) = 7,448.78 = 7,449

 

C. After 21 days

t = 21

f(x) = 15000 e-^(0.05 * 21)

f(x) = 5,249

 

D. After 5 weeks

t = 5 * 7 = 35

f(x) = 15000 e-^(0.05 * 35)

f(x) = 2,606.61 = 2607