Question

Biologists stocked a lake with 800 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6600 . The number of fish grew to 1020 in the first year.

a) Find a logistical model for the number of fish P(t) after t years
P(t)=
b) How long will it take for the population to increase to 3300 hhalf of the carrying capacity)?
It will take years.

Answer 1

Below

Explanation:

from 800 to 1020 is a 220/800 * 100% = 27.5% increase each year

P(t) = 800 ( 1 + .275)^t

3300 = 800 ( 1+.275)^t

3300 / 800 = 1.275 ^t LOG both sides

.615423 / LOG 1.275 = t = 5.83 years