Question

Number of aphids present per day

EXERCISE 1 Understanding Population Growth with optimal conditions (eg, unrestricted resources and low competition), some populations grow in a predicable pattern. Early growth is relatively slow, after which growth is rapid. This rapid, logarithmic phase of growth represents the organism's blotic potential, which is its maximal reproductive capacity if given unlimited resources, exponential growth. N=(a)(2) Where: N = the number of individuals of a given generation. a = the number of individuals present initially. n = number of generations. POPULATION SIZE(N) +++++ TIME (1) FIGURE 2 Graph demonstrating exponential growth Exercise 1. Theoretical example of exponential growth Image that on the first day of the month you have a single aphid on your tomato plant. The next day it produces a clone so that you now have 2 aphids on your plant, and on the third day each produces a clone so that there are 4 aphids on the plant, and so on. If each aphid produces clones every day of the month, how many aphids would you have feeding on your tomato plant end of 20 days? Calculate the growth of the aphid population over 20 days using the formula for exponential growth, and record the values below. - TABLE 1 Number of aphids present per day I Day 11 Day 2 2 Day 3 4 Day 4 T Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 S Day 11 Day 12 Day 13 Day 14 Day 15 Day 16 Day 17 Day 18 Day 19 Day 20 X

Answer 1

According the formula of the exponential growth,

N = (a)(2^n)

Where, the N is the number of individuals present at current time.

a is the initial population,

n is the number of generation.

Here, it is given that,

a = 1

n = 20

But as there is addition of only 19 generations till the 20th day, so we will use n=19. It is because there is no addition of new individuals on 1st day.

So,

N = (1)(2^19)

=1 × 524288

= 524288

Similarly the population at each generation can be calculated.

Day 1=1

Day 2=2

Day 3=4

Day 4=8

Day 5=16

Day 6=32

Day 7=64

Day 8=128

Day 9=256

Day 10=512

Day 11=1024

Day 12=2048

Day 13=4096

Day 14=8192

Day 15=16384

Day 16=32768

Day 17=65536

Day 18=131072

Day 19=262144

Day 20=524288

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