doubling time

Examples of doubling time in the following topics:

• Long Run Growth

  • Long run growth is the increase in the market value of the goods and services produced by an economy over time.
  • A growth rate of 2.5% per annum leads to a doubling of the GDP within 29 years, while a growth rate of 8% per annum (an average exceeded by China between 2000 and 2010) leads to a doubling of GDP within 10 years.
  • Note: an easy way to approximate the doubling time of a number with a constant growth rate is to use the Rule of 72.
  • For example, at a 10%, divide 72 by 10 to get a doubling time of 7.2 years.
  • The actual doubling time is 7.27 years, so the rule of 72 is a good rough approximation.

• Generation Time

  • Therefore, "local doubling" of the bacterial population occurs.
  • The doubling time is the generation time of the bacteria.
  • If growth is not limited, doubling will continue at a constant rate so both the number of cells and the rate of population increase doubles with each consecutive time period.
  • Death of cells as a function of time is rather unpredictable and very difficult to explain.
  • Note the Y-axis scale is logarithmic meaning that the number represents doubling.

• The DNA Double Helix

  • The DNA double helix looks like a twisted staircase, with the sugar and phosphate backbone surrounding complementary nitrogen bases.
  • DNA has a double-helix structure, with sugar and phosphate on the outside of the helix, forming the sugar-phosphate backbone of the DNA.
  • At this time it is possible a mutation may occur.
  • Most of the time when this happens the DNA is able to fix itself and return the original base to the sequence.
  • Native DNA is an antiparallel double helix.

• Composing in Basso-Continuo Style

  • If melody and alto share a note, that notehead is double-stemmed.
  • If the figure is 6/4, 5/3, or other chord of the fifth, double the bass pitch class.
  • Generally, do not double a variable scale degree or a chromatically altered pitch.
  • In basso continuo style, if the chord is properly voiced (correct pitch classes and correct doublings), two key principles of voice-leading will ensure good counterpoint between the voices most of the time:
  • Prefer repetition to steps, steps to leaps, and one leap at a time to several voices leaping at the same time.

• Hydrogenation

  • Addition of hydrogen to a carbon-carbon double bond is called hydrogenation.
  • The overall effect of such an addition is the reductive removal of the double bond functional group.
  • Regioselectivity is not an issue, since the same group (a hydrogen atom) is bonded to each of the double bond carbons.
  • The exact nature and timing of the last events is not well understood.
  • To a rough approximation, we see that each alkyl substituent on a double bond stabilizes this functional group by a bit more than 1 kcal/mole.

• Single Investment

  • Subscripts reflect the time with the final time period being T.
  • Interest rate, i, as a percentage, and the time indicates the number of years.
  • Accordingly, the product of the interest rate and time equals 72 in Equation 7.
  • The Chinese economy doubles every 7.2 years, or 72 ÷ 10.
  • How many years does the U.S. economy double in size?

• Epoxidation

  • Epoxidation of double bonds has proven to be an effective way of introducing oxygen functionality at both carbon atoms.
  • In this case note also the selective epoxidation of the more substituted double bond.
  • First, the Z-configuration of the double bond is preserved in the epoxide products.
  • A pink arrow indicates the bonding of this oxygen to a prochiral face of the double bond.
  • For the racemic alcohol in which R2 (or R3) is a cyclohexyl group, the S-enantiomer reacts over 100 times faster than the R-enantiomer, presumably due to steric hindrance of R2.

• Silicate Units, Silicate Chains, Silicate Sheets

  • The basic unit of silicate, [SiO4]4- tetrahedron, can form single and double chains and sheets.
  • Silicate minerals containing isolated [Si2O7]6− double tetrahedrons are called sorosilicates.
  • Asbestos (from Greek ἅ, unquenchable) is a group of fibrous silicate minerals containing double chains.
  • Mesothelioma is almost always fatal, with a median survival time of 11 months.
  • Ball-and-stick model of silicate double chains.

• Double Fertilization in Plants

  • Together, these two fertilization events in angiosperms are known as double fertilization .
  • Embryonic development is suspended after some time; growth resumes only when the seed germinates.
  • This is called a double fertilization.

• A short history of accounting and double entry bookkeeping

  • From time to time, a count of possessions would be made and compared to the records maintained by the scribe.
  • At any rate, the discovery of double-entry bookkeeping was undeniably important, because, as Wikipedia explains:
  • Double-Entry Bookkeeping is a system that ensures the integrity of the financial values recorded in a financial accounting system.
  • Here is a simple example to give you a feel for the way that double entry bookkeeping works:
  • First, a single transaction affects two accounts (a double-entry).