Given an initial population, $P _ { 0 } = 14,000$ , a renewal rate, R = 100, and a survival function, $S ( t ) = t e ^ { - 0.2 t }$ , with time t measured in years, determine the population at the end of 11 years. Round to two decimal places.
A) 8,120.55
B) 824.60
C) 58,646.60
D) 18,677.26

Question

Quizplus · Accepted Answer

The population at the end of 11 years can be calculated using the integral of the renewal rate multiplied by the survival function from 0 to 11, plus the initial population. The formula for the future population is $P(t) = P_0 + R \int_{0}^{t} S(t) dt$. Substituting the given values and solving the integral gives the population at the end of 11 years as approximately 18,677.26.

Given an Initial Population P0=14,000P _ { 0 } = 14,000P0​=14,000

Given an Initial Population $P _ { 0 } = 14,000$