Lesson 4.2

• Recall our lack of ability to solve exponential equations algebraically t
• We cannot manipulate both sides of the equation in the normal fashion
 us tools to be able add to or subtract from both sides
 multiply or divide both sides equations algebraically

• Consider solving    t 
25
 Previously used algebraic techniques
(add to, multiply both sides) not helpful
• Consider taking the log of both sides and using properties of logarithms

  
 t  log 25
 t  log 25 t
 log 0.886
  t
 log 0.886

• Consider solution of
1.7(2.1) 3x = 2(4.5) x
• Steps


Take log of both sides
Change exponents inside log to coefficients outside
 Isolate instances of the variable
 Solve for variable

• In 1992 the Internet linked 1.3 million host computers. In 2001 it linked 147 million.
 Write a formula for N = A e k*t where k is the continuous growth rate
• We seek the value of k
 Use this formula to determine how long it takes for the number of computers linked to double
2*A = A*e k*t
• We seek the value of t

• Change to the form Q = A*B t
Q
  e
0.4
t
• We know B = e k
• Change to the form Q = A* e k*t
Q

94.5(1.076) t
• We know k = ln B (Why?)

• May be a better mathematical model for some situations
• Bacteria growth
• Decrease of medicine in the bloodstream
• Population growth of a large group

• A population grows from its initial level of
22,000 people and grows at a continuous growth rate of 7.1% per year.
• What is the formula P(t), the population in year t?
 P(t) = 22000*e .071t
• By what percent does the population increase each year (What is the yearly growth rate)?
 Use b = e k

• In 1991 the remains of a man was found in melting snow in the Alps of Northern Italy.
An examination of the tissue sample revealed that 46% of the C body remained.
14 present in his


The half life of C
14 is 5728 years
How long ago did the man die?
• Use Q = A * e kt where A = 1 = 100%
 Find the value for k , then solve for t

• Suppose you want to know when two graphs meet y y
  t
3 0.25
 t
• Unsolvable by using logarithms
 Instead use graphing capability of calculator

• Lesson 4.2
• Page 164
• Exercises A
 1 – 41 odd
• Exercises B
 43 – 57 odd