Help with Initia Value Problem!!!!?

Question

Doctors are studying the spread of measles. Using the variable y to represent the proportion of a population affected by measles, and using t to represent time (days) they find the rate of spread of measles through a city can be modeled by the differential equation dy/dt = 0.2(0.6-y).
Suppose initially 10% of a cities population has measles.
(a) Solve this IVP.
(b) How long will it take before half the population are affected by measles?
(c) What is the long term proportion of the population which will be affected by measles?

Answer 1

5 dy/(0.6-y) = dt so
-5lnI 0.6-y I = t+C
I 0.6 -y I = k e ^-t/5
for t=0 y=0.10 so k= 0.5
0.6-y = 0.5 e^-t/5 and y= 0.6-0.5 e^-t/5
If y =0.5( 50%)
0.1/0.5 = e^-t/5 so t = -5*ln(0.1/0.5) = 8 days
lim y for t===> infinity =0.6(60%)

Answer 2

y' + 0.2 y = 0.12

y(t) = C e^(-t/5) + 0.6
y(0) = 0.1 => C+0.6 = 0.1 => C = -1/2

y(t) = 0.6 - 0.5e^(-t/5)

y(t) = 0.5
0.6 - 0.5 e^(-t/5) = 0.5
t = -5 * ln(0.2) = 8.047
Lim (t->infinity) y(t) = 0.6
60% of the population will be affected