How many viruses are there after seven days?Scientists culturing a virus find the number of viruses given by the function P(z)=2000+6000 lg(z + a),...

The number of live virus after z days is P(z) and this number
is given by:

P(z) =
2000+6000lg(z+a).

The  initial number of virus when z = 0, is given
by P(0) = 2000 +6000 log (0+a).

P(0) = 2572
given.

Therefore 2000 + 6000 log(0+a) = 2572
.

6000 loga = 2572 - 2000 =
572.

Therefore loga  =  572/6000
.

Therefore a = 10^(572/6000) =
1.24547

Therefore the given equation
becomes:

P(z) =
2000+6000log(z+1.24547).

Therefore the number of viruses after 7
days= P(7) = 2000+6000log(7+1.24547) = 2000+6000log(8.24547) = 2000+6000(0.916215) = 2000+5497 =
7497

So the number of virus after 7 days =
7497.