Question

Population growth problems BIDE model: No.1 N, +(B + 1) - ( D Rates: b = B/N; d = D/N: E) Net growth rate: R = b-d Exponential growth (discrete): N, NR* where R = 1+b-d Intrinsic rate of increase: r = InR Exponential growth (continuous): N:Noe -or-dN/dt = IN Logistic growth 1. Suppose a species of fish in a lake is modeled by a logistic population model with relative growth rate ofr 0.3 per year and carrying capacity of K = 10000. Using the equation below, if 2500 fish are initially introduced into the lake, how many fish are present after 5 years? Graph population growth over these 5 years. How long will it take to reach 8000 fish in the lake? 2. A population of 300 butterflies exhibits logistic growth. If the carrying capacity is 500 butterflies and r.0.1, what is the population growth rate? In other words, how many individuals are added to the population in one generation? 3. You collect the following information during a one-year period. There are at the start of the year 1,000 deer on the island; 120 deer die, 200 deer are born, 20 immigrate, and 10 emigrate. Calculate the growth rate. 4. The size of a hypothetical population is 25 organisms. Its maximum rate of increase is 1. The carrying capacity of the environment is 1,500 organisms for this species. What is the growth rate of this population (dN/dt)? What type of growth model does this population likely follow the next year? 5. The same population as in question 9, increased and reached 1,500 organisms. The intrinsic rate (max) of increase is still 1. What is the growth rate of the population in this case? What type of growth model does this population follow next year? 6. The population of Troy grows at a rate of 2% per year. The population in 1978 was 107,000 What is the predicted current population? When will the population reach 500,000? 7. The population of Stinktown is growing with a maximum rate of 30%, but its sanitary system can only handle 350,000 people. What is the population change (number of individuals added) based on a starting population of 10,000? 175,0007 275,000? Sketch the general population growth of this town.

Answer 1

1oooo Solo logistic population model | 1 - 9 ( P . Given de relative growth = 0.3 - carrying capacity, K= 10000 .. 0.3XN (10000 - N) Semelo ) Docenat berte si dhe ) = (3= d+ 14 dwe + dw = 3X10S+ By integrating at end we will get & N(0)=2500

N(I) = lot 31/10 34/10 +3 at it=s, N/5)= 104 1/10 e15/1043 = 5990.2 (oppeux. ) To reach N-8000 08.00 = 104 3to + 0.8 30 e3411043 2.4 = 0.2 034110 34/10 = 12 3t = ln 12 t = 10 11 12 t = 8.283 years) Approx. e 31/1043 Initial population - 3000 carrying capacity = 500 and le= 0.1 of logisitic growth model op - lex NCK-N) CK = 0.1XBoox (50o-300) days = 127 No. of individuals a populat geo with leate will be added in 1st generet" Ane soo