Population Dynamics, single species: In the forest lives a population of rabbits; each rabbit goes through four life stages: newborn, adolescent, mature, and old. Each year, 20% of the newborns live to be adolescent, 50% of the adolescents live to be mature, 80% of the mature rabbits live to be old. Per year, each mature rabbit produces 8 newborns and each old rabbit produces 12 newborns. (At the end of the year, none of the old rabbits survive.) Let Nk, Ak, Mk, and Dk represent the number of newborns, adolescents, mature, and old rabbits, respectively, after k years.(a) Write a system of equations which represents how the population grow each year, (b) Write this system as a matrix equation. (c) What is the largest real eigenvalues? What is the associated eigenvector? (d) As the population stabilizes, approximately how many newborns will there be for each old rab- bit? How many mature rabbits will there be for each old rabbit?

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk

80 the answer is 80

step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week