1. 4.5 Modeling with
Exponential and
Logarithmic
Functions
Mark 5:35-36 While he was still speaking, there came from the
ruler’s house some who said, “Your daughter is dead. Why trouble
the Teacher any further?” But overhearing what they said, Jesus
said to the ruler of the synagogue, “Do not fear, only believe.”

2. I recommend you read and understand all
the examples in this section ...
they are good ones!!

3. Exponential Growth Model

4. Exponential Growth Model
A population that has exponential growth
increases according to the model
rt
n ( t ) = no e

5. Exponential Growth Model
A population that has exponential growth
increases according to the model
rt
n ( t ) = no e
n ( t ) ↔ population at time t

6. Exponential Growth Model
A population that has exponential growth
increases according to the model
rt
n ( t ) = no e
n ( t ) ↔ population at time t
no ↔ original population

7. Exponential Growth Model
A 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

8. Exponential Growth Model
A 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

9. 1. (see handout)

10. 1. (see handout)
a) n ( t ) = 400e.4t

11. 1. (see handout)
a) n ( t ) = 400e.4t
b) n (10 ) = 400e .4(10)
≈ 21,800

12. 2. (see handout)

13. 2. (see handout)
a) 4700 = no e .55t

14. 2. (see handout)
a) 4700 = no e .55t
4700
no = .55(9)
e

15. 2. (see handout)
a) 4700 = no e .55t
4700
no = .55(9)
e
no ≈ 33

16. 2. (see handout)
a) 4700 = no e .55t
4700
no = .55(9)
e
no ≈ 33
b) n ( 20 ) = 33e .55(20)

17. 2. (see handout)
a) 4700 = no e .55t
4700
no = .55(9)
e
no ≈ 33
b) n ( 20 ) = 33e .55(20)
≈ 1,975,847

18. 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

19. 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

20. 3. (see handout)

21. 3. (see handout)
a) 2300 = 200e 18r

22. 3. (see handout)
a) 2300 = 200e 18r
23 18r
=e
2

23. 3. (see handout)
a) 2300 = 200e 18r
23 18r
=e
2
⎛ 23 ⎞
ln ⎜ ⎟ = 18r ln e
⎝ 2 ⎠

24. 3. (see handout)
a) 2300 = 200e 18r
23 18r
=e
2
⎛ 23 ⎞
ln ⎜ ⎟ = 18r ln e
⎝ 2 ⎠
⎛ 23 ⎞
ln ⎜ ⎟
⎝ 2 ⎠
=r
18

25. 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%

26. 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%

27. HW #10
A man who wants to lead the orchestra must
turn his back on the crowd.
Max Lucado