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How do we use logarithms

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How do we use logarithms

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    2. How do we use logarithms? pH level in blood slope of a beach speed of wind inside a tornado magnitude of an earthquake transport a substance into a human cell intensity of sound interest on money estimate the time of death

    3. pH level in blood. The pH of a patient’s blood can be calculated using the Henderson-Hasselbach Formula: pH = 6.1 + log10 (B/C) where B is the concentration of bicarbonate, and C is the concentration of carbonic acid.

    4. Slope of a beach! The slope, s, of a beach is related to the average diameter, d (in millimeters), of the sand particles on the beach by the formula: s=0.159 + 0.118log10 d If the sand is very coarse, the slope of the beach will be steeper than if the sand is fine.

    5. Tornado! The speed of the wind, S (in miles per hour), near the center of a tornado is related to the distance the tornado traveled, d (in miles), by the formula: S = 93 log10 d + 65

    6. Earthquake! The Richter scale is used to measure the magnitude, R, of an earthquake of intensity I is given by the formula: R = log10 I The intensity is a measure of the wave of energy of an earthquake per unit of area.

    7. Human Cells! The energy, E (in kilocalories per gram molecule), required to transport a substance from the outside to the inside of a living cell is given by the formula: E = 1.4(log C2 - log C1) C1 is the concentration of the substance outside the cell C2 is the concentration inside the cell.

    8. Sound ! The level of sound, B (in decibels), is related to the intensity of the sound, I (in watts per square cm.), by the formula: B = 10 log10 (I/I0) I is the intensity of the faintest sound that can be heard by human ears.

    9. Natural Logarithms ( ln) Natural logarithms are calculated in base e, which is also called the Euler number, named after Leonard Euler.

    10. Interest on $ MONEY! If interest is compounded quarterly, use the formula: A = P( 1+ r / n ) ^ nt If interest is compounded continuously, use the formula: A = Pe^ rt

    11. Amount of $ after 10 years at 5% interest.

    12. Amount of $ after 10 years at 5% interest

    13. Time of Death! To estimate the time of death of a human body, a coroner uses Newton’s law of cooling: Kt = ln(T-S)/(T0-S1) k is a constant, S is the temperature of the surrounding air, t is the time it takes for the body temperature to cool from the time of death.

    14. Credits Algebra 2, An Integrated Approach,D.C. Heath and Company Microsoft clip-art and pictures Stribling Funeral Home http://www.animfactory.com/ http://wwwpersonal.engin.umich.edu/~dkyser/weather/pics.htm Encyclopedia of World Biography, 2nd edition, Diderot and Forbes, 1998

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