Consider a pond with pond lilies that double everyday and it takes 30 days for the pond lilies to completely cover the pond. a. On what day will the pond be 1/4 covered? b. On what day will the pond be 1/2 covered? c. Does the size of the pond make a difference? d. What will begin to happen at one minute past the 30th day? e. If this pond were earth, and the lilies were people, what kind of environmental, social, and economic developments can be expected as the 30th day approaches? f. At what point (what day) would preventative action become necessary to prevent unpleasant events? g. If this pond were your city, state or country, and the lilies were people, considering all other life, at what day would you and your family like to live and have the highest quality of life? h. Based on your understanding, what corresponding day do you think we are at in the world today? The United States?

Step-by-step explanation:

To understand this question start from day 30 when the pond is completely covered. Before the 30th day, the pond must have half as many lilies. And if go another day back i-e 28th day, the pond will be 1/4 covered.

a. On what day will the pond be 1/4 covered?

Ans. 28th day

b. On what day will the pond be 1/2 covered?

Ans. 29th day

c. Does the size of the pond make a difference?

Ans. Yes, the bigger the size, the more room there will be for lilies

d. What will begin to happen at one minute past the 30th day?

Ans. The lilies in pond will start to wither and rot due to lack of space for other lilies to grow

e. If this pond were earth, and the lilies were people, what kind of environmental, social, and economic developments can be expected as the 30th day approaches?

Ans. Expanding the size of the pond or limiting the reproduction of lilies could be one of two alternative approaches to cater this issue.

f. At what point (what day) would preventative action become necessary to prevent unpleasant events?

Ans. Action becomes necessary before the 30th day approaches.

g. If this pond were your city, state or country, and the lilies were people, considering all other life, at what day would you and your family like to live and have the highest quality of life?

Ans. The quality of life is highest at the first day. The increase in number of lilies would reduce the quality of life, as limited space and water would be occupied by many lilies.

h. Based on your understanding, what corresponding day do you think we are at in the world today? The United States?

Ans. According to one study, the maximum number of humans earth can support is 10 billion and currently we are standing at 7 billion which is more than half of 10 billion. Considering the reproduction rate doubles everyday as in the example, we are standing midway on 29th day.

(a) on the 28th day, the pond will be 1/4 covered

(b) On 29th day, the pond will be 1/2 covered.

(c) Yes, the size of the pond makes a difference by accommodating the growing population of the pond lilies day after day.

(d) one minute after 30 days, the pond can no longer accommodate the pond lilies population. The will be overpopulation.

(e) As 30th day approaches, the people will start to readjust as the environmental, economical and social development will be at it peak as the population continue to grow

(f) At the 29th day, the preventive action become necessary to avoid unpleasant events that are associated with overpopulation

(g) My family and I will like to live on the 2nd day, to enjoy the highest qualities of life. At this time, the will be amenities with lesser population of people competing for it.

(g) In the world today, we are in the 29th day. Over the half of the earth's capacity of people's populations. That is, approximately 7billions people of 10billion people' earth total capacity.

Step-by-step explanation:

1st day, it doubled - (1*2^1)lilies

2nd day, (1*2^2)lilies

nth day, we have (1*2^n) lilies

On 30th day, the pond lilies will completely cover the pond. The number of the pond lilies will be (1*2^30) = 1073741824units

The pond will be 1/4 covered by 1073741824/4 = 268435456lilies at x day.

Therefore

268435456 = 1*2^x

Taking logarithm of both sides,

log(268435456) = log(2^x)

log(268435456) = xlog2

x = log(268435456)/log2

x = 28(That is, on 28th day)

The pond will be 1/2 covered by 1073741824/2 = 536870912lilies at y days

Therefore, 536870912 = 1*2^y.

Taking logarithm of both sides,

log(536870912) = log2^y

log(536870912) = ylog2

y = log(536870912)/log2

y = 29(That is, on 29th day)