Biologists stocked a lake with `500` fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be `9600`. The number of fish grew to 790 in the first year.

a)Find an equation for the number of fish `P(t)` after `t` years. Use a growth rate (`k`) value of three decimal places.
` P(t)=`  

b) How long will it take for the population to increase to `4800` (half of the carrying capacity)?
It will take   years.
You may enter the exact value or round to two decimal places.