88. A population increases from 25,000 to 26,000 during a period of one year. Take the difference between the starting number of 25,000 and the final number of 26,000 and divide by the starting number of 25,000. In other words, divide 1,000 by 25,000 = 0.04. Multiply this number by 100 to make it a percent. This is the annual percent increase for the population.
89. A population increases from 25,000 to 75,000 during an 18 year period. Take the difference between the starting number of 25,000 and the final number of 75,000 and divide by the starting number of 25,000. Convert this decimal value into a percent. This is the percent increase of the population during an 18 year interval.
90. Subtract Kenya's death rate per 1,000 (12) from Kenya's birth rate per 1,000 (52). Divide this difference of 40 by 1000. Multiply your answer by 100 to convert this decimal value into a percent.
91. To find the doubling time, divide 0.695 by the annual growth rate of Kenya (previous question). Use the decimal value for growth rate. See the following JavaScript link:
92. To find the doubling time of your money, divide 0.695 by the annual growth rate of 10 percent or .10. [Use the decimal value for growth rate.] See the following JavaScript link:
93. Use the exponential population growth equation for this question: N = N_{o} e^{rt}
N_{o} = 1.0; r = 10 percent or 0.10; t = 30 years; e = approx. 2.71828

94. Use the exponential population growth equation for this question: N = N_{o} e^{rt}
N_{o} = 1.0; r = 3 percent or 0.03; t = 100 years; e = approx. 2.71828

Your number increase is approximately 1 to 20 during the 100 year period. Take the difference between the starting number of 1.0 and the final number of 20 and divide by the starting number of 1.0. In other words, divide 19 by 1.0 and convert this number into a percent.
95. Use the exponential population growth equation for this question: N = N_{o} e^{rt}
N_{o} = 1.0; r = 1 percent or 0.01; t = 100 years; e = approx. 2.71828

Your number increase is approximately 1 to 3 during the 100 year period. Take the difference between the starting number of 1.0 and the final number of 3 and divide by the starting number of 1.0. In other words, divide 2 by 1.0 and multiply by 100 to make the number a percent.
96. To find the doubling time, divide 0.695 by the annual growth rate of 2 percent or .02. [Use the decimal value for growth rate.]
97. Use the exponential population growth equation for this question: N = N_{o} e^{rt}
N_{o} = 5,000,000,000; r = 2 percent or 0.02; t = 112 years; e = 2.71828

98. It really helps if you have a math calculator with logarithmic functions for this question. Here is how you set it up:
40 billion = 5 billion e^{0.02 (t)}
8 billion = e^{0.02 (t)}
0.02 (t) = ln 8 ln 8 = natural log of 8 = 2.07944
t = ln 8 divided by 0.02 = 103.9 or approx. 104 years

99. Because wolffia populations increase so rapidly, use days rather than years. To find the growth rate in days, divide 0.695 by the doubling time in days (1.25). Use the decimal value for doubling time.
100. Use exponential population growth equation for this question: N = N_{o} e^{rt}
N_{o} = 1.0; r = 56 percent or 0.56; t = 125 days; e = 2.71828

101. Use population growth as a geometric progression for this question:
2 people 20 yrs 6 people 20 yrs 18 people 20 yrs 54

Starting with 2 people (one heterosexual couple), in 20 years they give rise to 6 people. In other words, the original female has 6 offspring (3 boys and 3 girls). Of the resulting 6 people, 3 of them are girls. In the next 20 year interval, each of the 3 girls has 6 offspring resulting in 3 x 6 = 18 people. Of the resulting 18 people, 9 of them are girls. In the next 20 year intervel, each of the 9 girls has 6 offspring resulting in 9 x 6 = 54 people. After a total of three generations (60 years), the total number of people is 2 + 6 + 18 = 54 = 80.
102. Use population growth as a geometric progression for this question:
2 people 30 yrs 6 people 30 yrs 18 people

Starting with 2 people (one heterosexual couple), in 30 years they give rise to 6 people. In other words, the original female has 6 offspring (3 boys and 3 girls). Of the resulting 6 people, 3 of them are girls. In the next 30 year intervel, each of the 3 girls has 6 offspring resulting in 3 x 6 = 18 people. After a total of two generations (60 years), the total number of people is 2 + 6 + 18 = 26.
103. In this question, population growth as a simple geometric progression does not work because we are including the children of the daughters and sons in the total descendants of Jack and Jill. [Of course, the sons have spouses who actually bear the children.] In the previous examples of simple geometric progressions, we only considered the offspring of females in the calculations.
Jack & Jill 20 yrs 2 children 20 yrs 4 grandchildren 20 yrs 8 great grandchildren

Starting with Jack & Jill (one heterosexual couple), in 20 years they give rise to 2 children. In other words, Jill has two offspring (1 boy and 1 girl). During the next 20 years, their son and daughter marry and each has two offspring resulting in four grandchildren (2 boys and 2 girls). During the next 20 years, their four grandchildren marry and each has two children resulting in eight great grandchildren. After a total of three generations (60 years), the total number of descendents is 2 + 4 + 8 = 14.
In the following example, the generation time is increased to 30 years, so that there are only two generations possible during a 60 year interval.
Jack & Jill 30 yrs 2 children 30 yrs 4 grandchildren

Starting with Jack & Jill (one heterosexual couple), in 30 years they give rise to 2 children. In other words, Jill has two offspring (1 boy and 1 girl). During the next 30 years, their son and daughter marry and each has two offspring resulting in four grandchildren (2 boys and 2 girls). After a total of two generations (60 years), the total number of descendents is 2 + 4 = 6.
104. By increasing the generation interval from 20 years to 30 years in the previous question, the total number of descendants decreases from 14 to 6. To calculate the percent decrease, subtract 6 from 14 and divide this number by the starting number of 14. In other words, 8 divided by 14 = 0.571. Multiply by 100 to convert this number into a percent = 57.1 percent or rounded off = 57 percent. Increasing the generation interval from 20 years to 30 years reduces the total number of descendants by 57 percent!
105. After working on this exam for 50 minutes, the world population has increased by 9,000 people. What is the annual percentage growth rate at this time? See the following link to answer this question:
