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0411 ch 4 day 11
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0411 ch 4 day 11

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0411 ch 4 day 11 0411 ch 4 day 11 Presentation Transcript

  • 4.5 Modeling with Exponential and Logarithmic FunctionsMark 5:35-36  While he was still speaking, there came from theruler’s house some who said, “Your daughter is dead. Why troublethe Teacher any further?” But overhearing what they said, Jesussaid to the ruler of the synagogue, “Do not fear, only believe.”
  • I recommend you read and understand all the examples in this section ... they are good ones!!
  • Exponential Growth Model
  • Exponential Growth ModelA population that has exponential growth increases according to the model rt n ( t ) = no e
  • Exponential Growth ModelA population that has exponential growth increases according to the model rt n ( t ) = no e n ( t ) ↔ population at time t
  • Exponential Growth ModelA population that has exponential growth increases according to the model rt n ( t ) = no e n ( t ) ↔ population at time t no ↔ original population
  • Exponential Growth ModelA population that has exponential growth increases according to the model rt n ( t ) = no e n ( t ) ↔ population at time t no ↔ original population r ↔ rate of growth
  • Exponential Growth ModelA population that has exponential growth increases according to the model rt n ( t ) = no e n ( t ) ↔ population at time t no ↔ original population r ↔ rate of growth t ↔ time
  • 1. (see handout)
  • 1. (see handout) a) n ( t ) = 400e.4t
  • 1. (see handout) a) n ( t ) = 400e.4t b) n (10 ) = 400e .4(10) ≈ 21,800
  • 2. (see handout)
  • 2. (see handout) a) 4700 = no e .55t
  • 2. (see handout) a) 4700 = no e .55t 4700 no = .55(9) e
  • 2. (see handout) a) 4700 = no e .55t 4700 no = .55(9) e no ≈ 33
  • 2. (see handout) a) 4700 = no e .55t 4700 no = .55(9) e no ≈ 33 b) n ( 20 ) = 33e .55(20)
  • 2. (see handout) a) 4700 = no e .55t 4700 no = .55(9) e no ≈ 33 b) n ( 20 ) = 33e .55(20) ≈ 1,975,847
  • 2. (see handout) Do you think the a) 4700 = no e .55t population would ever 4700 get to that value? no = .55(9) e no ≈ 33 b) n ( 20 ) = 33e .55(20) ≈ 1,975,847
  • 2. (see handout) Do you think the a) 4700 = no e .55t population would ever 4700 get to that value? no = .55(9) e Read about no ≈ 33 Logistic Growth on page 392 b) n ( 20 ) = 33e .55(20) ≈ 1,975,847
  • 3. (see handout)
  • 3. (see handout) a) 2300 = 200e 18r
  • 3. (see handout) a) 2300 = 200e 18r 23 18r =e 2
  • 3. (see handout) a) 2300 = 200e 18r 23 18r =e 2 ⎛ 23 ⎞ ln ⎜ ⎟ = 18r ln e ⎝ 2 ⎠
  • 3. (see handout) a) 2300 = 200e 18r 23 18r =e 2 ⎛ 23 ⎞ ln ⎜ ⎟ = 18r ln e ⎝ 2 ⎠ ⎛ 23 ⎞ ln ⎜ ⎟ ⎝ 2 ⎠ =r 18
  • 3. (see handout) a) 2300 = 200e 18r 23 18r =e 2 ⎛ 23 ⎞ ln ⎜ ⎟ = 18r ln e ⎝ 2 ⎠ ⎛ 23 ⎞ ln ⎜ ⎟ ⎝ 2 ⎠ =r 18 r ≈ .13568 or ≈ 14%
  • 3. (see handout) a) 2300 = 200e 18r 23 18r =e b) .14t P = 200e 2 ⎛ 23 ⎞ ln ⎜ ⎟ = 18r ln e ⎝ 2 ⎠ ⎛ 23 ⎞ ln ⎜ ⎟ ⎝ 2 ⎠ =r 18 r ≈ .13568 or ≈ 14%
  • HW #10A man who wants to lead the orchestra mustturn his back on the crowd. Max Lucado