Question

A species of fish was added to a lake. The population size Pt of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t) = 1000+(12e^−0.34t)where t is the number of years from the time the species was added to the lake.
Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary.

Answer 1

Answer:

1,012 ; 1,001

Step-by-step explanation:

Given the population function :

P(t) = 1000+(12e^−0.34t)

where t is the number of years from the time the species was added to the lake.

Initial population size of the species ; that is the population at year 0

At time, t = 0

P(0) = 1000+(12e^−0.34(0))

= 1000 + (12e^0)

= 1000 + 12(1)

= 1012

Initial population = 1,012

Population after 9 years :

P(9) = 1000+(12e^−0.34(9))

= 1000 + (12e^-3. 06)

= 1000 + (12×0.0468876)

= 1000 + ( 0.5626523)

= 1000.5626

= 1001 ( nearest whole number)