Transcript Lesson 4.8 with work

FINAL EXAM!!!!
Tuesday May 7th
Wednesday May 8th
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?
Newton’s Law of Cooling
u0 = Initial temperature of the heated object
k = negative
constant
u (t )  T  (u0  T )e kt
u = temperature at a given
time, t
t = time
T = constant temperature of the surrounding area
Newton’s Law of Cooling Practice
An object is heated to 100C (degrees Celsius) and is then
allowed to cool in a room who’s air temperature is 30C.
If the temperature of the object is 80C after 5 minutes, when
will its temperature be 50C?
FINAL EXAM!!!!
Tuesday May 7th
Wednesday May 8th
Section 4.8:
Exponential
Growth &
Decay
Homework #23:
pg 334
#5, 9, 13 (a& b), 21
STUDY GUIDE!