Question

The number of people expected to have a disease in t years is given by

Answer 1

If we let a = 9,
y(t) = A x 3^(t/9)

(i) If y(t) = 1000 a t = 0, then
1000 = A (3)^(0/a)
A = 1000

(ii) At t= 5
y(5) = 1000 (3)^(5/9)
y(5) = 1841

(iii) At y(t) = 100,000
100,000 = 1000 (3)^(t/9)
t = 37.7 years

(iv) Taking the derivative and substituting, t = 0 , and t = 10
for t = 0
dy/dt = 122 people/year

for t = 10
dy/dt = 414 people/year