The half life of a substance is the time it takes for 1/2 of the substance to decay, metabolize, or be used up. For example, if 1/2 of a drug is metabolized in 3 hours, after 6 hours 1/4 of the drug is left and 3/4 of the drug has been used:
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What changes when D_0 changes? What changes when h changes?
|Manipulative 1 - Half Life Created with GeoGebra.|
The half life of a radioactive substance is 3 hours. The initial amount is 3 grams. How long before only 0.6 grams is left?
|1||Start with the half-life formula.|
|2||Fill the values into the formula. The initial amount D0 = 3. The half-life h = 3. The amount left after 3 hours D = 0.6. Solve for t.|
|3||Use the multiplication property of equality to multiply both sides of the equation by 1/3.|
|4||Use the logarithm to convert the equation from exponential form to logarithmic form. The definition of a logarithm is logab = c if and only if ac = b. In this case a = 1/2, b = 0.2 and c = t/3.|
|5||Use the multiplication property of equality to multiply both sides of the equation by 3.|
|6||Use the change of base formula to convert the logarithm to base 10. The change of base formula is . In this case, a = 1/2, x = 0.2 and b = 10.|
|7||Substitute the values of the logarithms into the equation. log100.2 ≈ -0.69897. log100.5 ≈ -0.30103.|
|8||t ≈ 6.9658||Calculate the approximate value of t. It will take about 7 hours for only 0.6 grams to be left.|
|Table 2: Half life example.|
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