Applications of Exponential Models

In humans, caffeine acts as a central nervous system stimulant, temporarily warding off drowsiness and restoring alertness.central nervous system It is the world's most widely consumed psychoactive drug, but unlike many other psychoactive substances, it is legal and unregulated in nearly all parts of the world. psychoactive drug Beverages containing caffeine, such as coffee, tea, soft drinks, and energy drinks, enjoy great popularity. coffeeteasoft drinksenergy drinks In North America, 90% of adults consume caffeine daily.

Caffeine is completely absorbed by the stomach and small intestine within 45 minutes of ingestion. After ingestion it is distributed throughout all tissues of the body.

Half Life “half Life” is the unit we use to measure exponential decay. “Half life" is the time that passes until the quantity is half the original For example, suppose you drink 80 mg of caffeine, and it take 5 hours for your body to reduce the amount of caffeine to 40 mg. The Half Life of caffeine would be 5 hours.

The Half-Life of caffeine—the time required for the body to eliminate one-half of the total amount of caffeine consumed at a given time—varies widely among individuals according to such factors as age, liver function, pregnancy, some concurrent medications, and the level of enzymes in the liver needed for caffeine metabolism. In healthy adults, caffeine's half-life is approximately 3–4 hours.

You consume a RockStar cola which contains 300 mg of caffeine. 20 mg of caffeine is considered tolerable. How much is left in your system after 6h,12h,18h

Changes in a population of Paramecium over a six day period Each individual in the population divides once per day.

A f = A i (2) n

Exponential Decay Iodine – 131 is used to determine if a person has a thyroid deficiency.

The thyroid (from the Greek word for "shield", after its shape) is one of the larger endocrine glands in the body. It is a double-lobed structure located in the neck and produces hormones, principally thyroxine (T4) and triiodothyronine (T3), that regulate the rate of metabolism and affect the growth and rate of function of many other systems in the body. The hormone calcitonin is also produced and controls calcium blood levels. Iodine is necessary for the production of both hormones. Hyperthyroidism (overactive thyroid) and hypothyroidism (underactive thyroid) are the most common problems of the thyroid gland. Specialists are called Thyroidologists.endocrine neckhormonesthyroxinetriiodothyroninemetabolismcalcitoninHyperthyroidismhypothyroidismThyroidologists

Iodine – 131 is injected into the patient. A healthy thyroid will absorb all the iodine. An exponential equation will tell them how much iodine to look for.

A L = A O 1 2 t 8.2 A L = the amount of iodine left A O = the original amount of iodine t = the elapsed time in days

How long should it take 80mg of iodine to decay into 5 mg?

Pg 17 #10 Pg 24 #13,#14,#15,#16 Pg 26 #1