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

94. Use the exponential population growth equation for this question: N = N_o e^rt

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

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

98. It really helps if you have a math calculator with logarithmic functions for this question. Here is how you set it up:

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

101. Use population growth as a geometric progression for this question:

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:

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.

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.

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:

 1.   Plant Succession  

123. This carrying capacity is based of 0.25 acre of land per person per year and 10 billion acres of tillable land. Simply divide 10 billion by 0.25.

124. When will the world human population reach 40 billion?

127. A food chain decreases from 10,000 pounds of grass to 1500 pounds of grasshoppers. Take the difference between the starting number of 10,000 and the final number of 1500 and divide by the starting number of 10,000. Convert this decimal value into a percent. This is the percent decrease.

128. A geometric progression is a simplified way to show exponential population growth. Starting with one couple, assume that every female has 8 children (4 boys and 4 girls). The following table compares the population growth in 7 generations. The original couple has 8 children, four of which are girls which give rise to 8 children (4 x 8 = 32). Sixteen of the 32 children are girls which give rise to 128 children (16 x 8), etc. This is an exponential increase in which the population quadruples each generation. For example, the 7th generation is exactly four times larger than the sixth generation, and the 6th generation is exactly four times larger than the fifth generation, etc.

133. The efficiency of alcoholic fermentation. Since two molecules of ATP are produced for every molecule of glucose, a simple percent decrease can be used to show the percent efficiency of alcoholic fermentation. 686 kcal in a mole of glucose decreases to 16 kcal in two moles of ATP. Take the difference between the starting number of 686 and the final number of 16 and divide by the starting number of 686. 670 divided by the starting number of 686 = 0.98 or 98 percent. Therefore, the efficiency of alcoholic fermentation relative to energy in glucose and ATP is about 2 percent.

134. The larva of the Mexican jumping bean moth is a seed predator of the Mexican jumping bean shrub. The Mexican jumping bean shrub does not benefit from the jumping bean adult moth or its larval stage. All the other examples in the question are genuinely mutualistic in which both symbionts benefit from the relationship.

140 and 141. The following link about logistic population growth and carrying capacity explains these two questions.

142. The following link explains the answer to this question.

143. See the following link for an explanation of this question.

158. To find the doubling time, divide 0.695 by the annual growth rate of the world during the 1980s. Use the decimal value for growth rate. See the following JavaScript link:

160. See the following link for an explanation of this question.

162. You can use a simple proportion to solve this problem. If aerobic respiration produces 38 molecules of ATP with an efficiency of 44 percent, how many molecules of ATP would be produced with an efficiency of 100 percent? 38 molecules are to 44 percent as X molecules are to 100 percent. X = 38 x 100 divided by 44 = 86.

163. To find the annual growth rate, divide 0.695 by the doubling time of 10 years. Use the decimal value for doubling time. Multiply the decimal value for growth rate by 100 to obtain a percent.

166. To find the answer to question #166, please see the following link:

176. The numerical values in this question are twenty times greater than the example shown at the following link.

178. The answer for this question is explained at the following link.

179, 180 and 181. The answers for these three questions are explained at the following link.

185. The enrollment increased from 5,000 to 30,000 during a 30 year period. Take the difference between the starting number of 5,000 and the final number of 30,000 and divide by the starting number of 5,000. Convert this decimal value into a percent. This is the percent increase in the enrollment at Palomar College between 1972 and 2002.

191. The answer for this question is explained at the following link.

195. Subtract the death rate per 1,000 (12) from the birth rate per 1,000 (15). Divide this difference of 3 by 1000. Multiply your answer by 100 to convert this decimal value into a percent.

196. Use exponential population growth equation for this question: N = N_o e^rt

198. To find the doubling time, divide 0.695 by the annual growth rate of the U.S. population. Use the decimal value for growth rate. See the following JavaScript link:

203 - 209 The answer for these questions are explained at the following link.

212. Starting with the original heterosexual couple of 2, only the female bears offspring that comprise the next generation.

216 The answer for this question is explained at the following link.

217 The answer for this question is explained at the following link.