Transcript Section 4.8: Exponential Growth & Decay

Section 4.8:
Exponential
Growth &
Decay
Compounded Interest Review
An initial deposit is made in a savings account for which the
interest is compounded continuously. The balance of the account
will quadruple in 80 years. When will the balance of the account
reach $41,000 if the initial deposit was $8,000?
Exponential Growth and Decay
The amount A of an object present at time t is given by
A(t)  Aoe
kt
where A0 is the original amount of the object and k is the rate
of decay or growth (k > 0 if growth and k < 0 if decay)

k>0
k<0
Bacterial Growth
A colony of bacteria grows according to the law of uninhibited
growth. If 100 grams of bacteria are present initially, and 250
grams are present after two hours, how many will be present
after 4 hours?
Half-Life
The half-life of Uranium-234 is 200,000 years. If 50 grams of
Uranium-234 are present now, how much will be present in 1000
years (Half-life is the time required for half of a radioactive
substance to decay).
Bacterial Growth Practice
A colony of bacteria starts with 100 bacteria and increases
according to the law of uninhibited growth.
a) If the number of bacteria doubles in 3 hours, find the
function that gives the number of cells in the culture.
b) How long will it take the size of the colony to triple?
c) What is the population of the bacteria after 8 hours?
Logistic Growth and Decay Models
In logistic models, the population P after time t obeys
c
P(t) 
bt
1 ae
where a, b, and c are constants with c > 0, and c
represents the carrying capacity.

b>0
b<0
Logistic Growth
The logistic growth model
500
P(t) 
1 6.67e0.2476t
represents the amount of bacteria (in grams) after t days
a) What is the carrying capacity?

b) What was the initial amount of bacteria?
Logistic Growth
The logistic growth model
500
P(t) 
1 6.67e0.2476t
represents the amount of bacteria (in grams) after t days
c) When will the amount of bacteria be 300 grams?

Section 4.8:
Exponential
Growth &
Decay
Homework:
pg 334 – 336
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