Module 14 Pre-Lecture Notes

The body eliminates different drugs differently. Some drugs (such as alcohol) are eliminated at a constant rate. These are called zero-order drugs. The amount of a zero-order drug in the body can be modeled by a y = mx + b equation, a linear equation.

More drugs exhibit exponential decay. These are called first-order drugs. Exponential decay does not have a constant rate of elimination. Instead it has a constant percent. Caffeine is a first order drug. If you drink a typical soft drink with 48 mg of caffeine, 3 hours later half of the caffeine will be eliminated (now your body has 24 mg). In another 3 hours, half of that caffeine will be eliminated (now your body has 12 mg). This process will continue until less than 1 molecule of caffeine remains. Notice that fewer mg of caffeine were eliminated in the 2^nd three hour time block, but the percent (50%) remained the same.

Linear Models vs Exponential Models: Openstax College Algebra - Section 6.1

• Explain linear growth:

• Explain exponential growth:

• Define:
  • Percent change:

• Exponential growth:

• Exponential decay:

Defining Exponential Growth:

• f(x) = ab^x

a = __________________________________________

b = __________________________________________

How is the value of "b" calculated?

The number e:

• What is the approximate decimal value for e? ____________________________________
• Who discovered e? ____________________________________
• What kind of number is it? _____________________________________________
• What kind of growth is modeled with e? ______________________________________
• Explain the meaning of the parts of the continuous growth/decay formula.

A(t) = Pe^rt

• P = _________________________
• r = ___________________________
• t = ___________________________

How do you tell if it is a growth or decay model?

Common Exponential Models:

1. Exponential Model: P(t) = P₀e^kt models how many populations grow and how many medications are eliminated from the body. Define what each variable stands for:

P(t) = population at a specific time t. Function notation for the y variable

P₀ = the starting population

e = ____________________________________________________________ (from above)

k = relative growth rate; a percent written in decimal form t = the time

• If k is positive the population is growing, if k is negative the population is decaying

2. Doubling Time Model: P(t) = P₀2^(t/d) (complete based on the Exponential Model in part 1 of this section)

P(t) = ____________________________________________________

P₀ = ________________________________________ t = ___________________________

d = the length of time required for a population to double

3. Half-life model: P(t) = P₀0.5^(t/d) (complete based on the Exponential Model in part 1 in this section)

P(t) = ____________________________________________________

P₀ = ________________________________________ t = ___________________________

d = the length of time required for the population to decrease by half