Pass up your homework
and clear your desk for
the QUIZ
Solve for x:
x
e =
72
Solve for x:
x
5 =
17
Solve for x:
100e(0.05x) = 300
Solve for x:
7 - 3e-x = 2
Solve for x:
e
2x
 5e  6  0
x
Solve for x:
8
2x 1
 39
x 1
General Formula for
Population Growth/Decay
Pn = P0(1 ± r
n
)
The population of Eagle City was 10,000 people in
1900. It has been increasing at a steady rate of 2.5%
per year.
1.
2.
Let n = the number of years since 1900 and P(n) = the population of
Eagle city. Write a function P(n) that defines the population in terms of
the years since 1900.
Use your function from #1 to predict the population of Eagle City at the
end of 1937.
3. Use your equation to predict when the population will be 100,000 people.
The population of Trojanville in the year 2000 was
235,000 and continues to decrease at the rate of
1.5% every year.
1.
Write a function P(n) that defines the population in terms of the
years since 2000.
2.
Use your function from #1 to predict the population of Trojanville
after 5 years
3.
Use your equation to predict when the population will be 200,000
people.
The population of Smallville was 678 in 1955 and 1,410
in 1970. Assuming exponential growth, what would be
the growth rate per year?
General Half-life equation
1
Pn  P0  
2
Initial
population
n
half life
Suppose the half-life of a certain radioactive substance is
20 days and that there are 5 grams present initially.
1.
Write a function for the amount of substance that is present
after t days.
2.
Use your function to predict when there will only be 1 gram
left.
3.
Use your function to predict the amount of substance present
after 30 days.
The half-life of a certain substance is 65 days and there are
3.5grams present initially. When will there be 2 grams left?
General Interest Equations
Compound interest
nt
r

Pn  P0  1  
 t 
Compound Continuously
Pn  P0e
rn
You deposit $5000 in a trust fund that pays 7.5%
interest compounded monthly.
1.
Write a function for the amount of money that is present after n years.
2.
How much time will it take for your money to double?
You deposit $1000 in a savings account that earns 4%
interest compounded continuously
1. How much money will you have in 10 years?
2. How long will it take for you to accumulate $3200
Determine when an investment of $1500 accumulates to a
value of $2280 if the investment earns interest at a rate
of 7%APR compounded quarterly.