An epidemic is modelled by $y=5e^{0.3t}$. Find another expression for $t ≥ 2$

Question

I have attached a photo of the question to avoid mistakes in explaining. I am referring to part b in particular. I haven't been able to get the right answer, which is $2.26e^{0.3t}$.

How should I be thinking about this?

Thanks in advance

Answer 1

The number of patients in hospital equals the number of patients infected - number of patients discharged.

The number of patients discharged is the same as the number of patients who were infected 2 or more weeks ago.

for $t>2, y = 5e^{0.3t} - 5e^{0.3(t-2)}$

$y = 5e^{0.3t}(1-e^{-0.6})\\ y = 5(0.45)e^{0.3t}\\ y = 2.26 e^{0.3t}$