SOLUTION: Using the formula for exponential population growth: New population size = r*N + N, calculate the new population size in the data table below: Number of generations Populatio

Algebra ->  Equations -> SOLUTION: Using the formula for exponential population growth: New population size = r*N + N, calculate the new population size in the data table below: Number of generations Populatio      Log On


   

Question 1118985: Using the formula for exponential population growth: New population size = r*N + N, calculate the new population size in the data table below:
Number of generations Populations size (N) Growth rate
0 10 0.6
1 16 0.6
2 ??

a. 22.6

b. 24.2

c.25.6

d. 30.4

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Generation 0: N = 10; r = 0.6

Generation 1: N(new) = r*N+N = 0.6(10)+10 = 6+10 = 16; r = 0.6

Generation 2: N(new) = r*N+N = 0.6(16)+16 = 9.6+16 = 25.6

Answer c

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I hope this problem is from an introductory lesson on exponential growth. The recursive process used is extremely inefficient; to find the population after 20 generations you would have to perform the defined calculation 20 times.

It is far more efficient to use an explicit formula for the population after n generations. The recursive formula for the new population size,

r%2AN%2BN

can be written as

N%28r%2B1%29 or N%281%2Br%29;

then the population after n generations is simply the beginning population, multiplied by the "growth factor" (1+r) n times:

P%28n%29+=+N%281%2Br%29%5En

For your problem the populations after 1 and 2 generations are then

P%281%29+=+10%281.6%29+=+16
P%282%29+=+10%281.6%29%5E2+=+10%282.56%29+=+25.6

To find the population after 10 generations by the recursive method would be very tedious; with this method it is a single calculation:

P%2810%29+=+10%281.6%29%5E10+=+1100 (to the nearest whole number)