12H - Applications of exponential and logarithmic functions
Exponential growth and decay
Exponential growth and decay model have the general equation \(y=Ae^{kt}\) where \(t\geq 0\).
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12H - Example 1: Modelling eXPONENTIAL decay (CAS)
Gold is an important metal due to its physical and chemical properties, one of which is its stability. However, not all forms of gold are stable. One isotope, Gold-198, undergoes radioactive decay. In one experiment, a scientist observed that after 21 hours, only 80% of the initial amount of gold remained. Determine the half-life, the time taken for half of a substance to decay, of Gold-198. State your answer, in days, correct to 2 decimal place.
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12H - Example 1: Video solution
12H - Example 1: Practice
Question 1: ABC 12H - Example 1: Solutions
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12H - Example 2: Modelling exponential growth (CAS)
The number of koalas, \(N\), in a national park can be modelled by the equation \(N(t)=708(2.4)^{-(t+1)}\), where \(t\) is the number years since January 1, 2004.
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12H - Example 2: Video solution
12H - Example 2: Practice
Question 1: ABC 12H - Example 2: Solutions
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Surge models
Other models also include exponential or logarithmic functions. One such model is the surge model which is often used to model that uptake and elimination medicine in the body.
12H - Example 3: surge models (CAS)
The amount of aspirin absorbed into the bloodstream of an adult is modelled by the equation \(M(t)=80t e^{-0.5t}\), where \(M\) is the mass of aspirin, in milligrams, and \(t\) is the time, in hours, after the tablet is ingested.
A pharmacist is interested in the maximum amount of aspirin absorbed into the bloodstream
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12H - Example 3: Video solution
12H - Example 3: Practice
Question 1: ABC 12H - Example 3: Solutions
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