Could u help me with this question.

Question

The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by

N (t) = a / 1+ be^ -kt

a. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b

b. If the rumour is initially spreading at the rate of 500 people per day, find k.

Thanks.

for a)
initially ---> t=0
so 50 = a/(1 + be^0)
50 = a/(1+b)
a=50 + 50b ----- (#1)

I will interpret "eventually" to mean t --> ∞

then e^(-large) ---> 0

and 300000=a/(1+0), so a=300000
putting this back in #1 gives b=5999

so N(t) = 300000/(1 + 5999e^-kt)^-1

for b)
N'(t) = -300000((1 + 5999e^-kt)^-2)(e^-kt)(-k)

"initially" the rate is 500 means
500 = -300000(1+5999)^-2 * (1)(-k)
..
..
I got k=10, check my arithmetic please