Algebra 3: VIDEO Notes:
6.7 Interest Formulas
I. Appreciation / Depreciation
A= Current Amount or Value
A 0 = Initial Amount or Value
r = rate of interest ( as a decimal)
t = period of time
II. Continuous Compounding:
A = Amount of money earned
P = amount invested
r = annual interest rate (decimal)
t = period of time (in years)
A=Pe
(r t )
Appreciation: A = A0(1+ r)t
Depreciation: A = A0(1 –
Find the amount in a continuously compounded
account for the principal of $2000. ,an annual interest
rate of 4.8% and over 2 years.
r)t
What will a $90,000 house cost 5 years
From now if the price appreciation for homes over
that period averages 3% annually?
In how many years will it take for an initial investment
of $10,000 to grow to $25,000? Assume a rate of
interest of 6% compounded continuously.
𝒓 (𝒏 𝒕 )
III. Compound Interest:
A = P ∙ (𝟏 + 𝒏)
A = Amount of money earned
P = amount invested
r = Annual interest rate (decimal)
t = period of time (in years)
n = number of times per year
Annually: ______ per year
Monthly: __________ per year
Semiannually: _________ per year Daily: _____________ per year
Quarterly: ___________ per year
Annum: per ___________
How much money will result from $100 invested at 4%
compounded quarterly after a period of 2 years?
Find the principal needed to get $100 after
2 years at 6% compounded monthly.
Section 6.8
I.
Exponential Growth and Decay Models
Uninhibited Growth:
N(t) = N0 e (k t)
,
Uninhabited Radioactive Decay:
k>0
N(t) = number of cells in culture
N0 = initial number of cells
t = amount of time passed
k = positive growth rate of cells (as decimal)
The size P of a certain insect population at time t (in
days) obeys the function
P(t) = 500
e0.02t.
A(t) = A0 e (k t) ,
k<0
A(t) = amount of radioactive material
A0 = original amount of material
t = time material is present
k = negative rate of decay (as decimal)
Strontium 90 is a radioactive material that decays
according to the function A(t) = A0 e -0.0244 t .
A scientist has a sample of 500 grams initially.
The initial population, when t=0 is _______________
What is the decay rate of strontium 90? ___________
What is the growth rate of the population? ________
How much strontium 90 is left after 10 years?
What is the population in 10 days?
When will 400 grams of strontium 90 be left?
When will the population reach 800?
What is the half-life of strontium 90?
When will it double?
20. A release of radioactive material into the atmosphere occurred at a nuclear plant accident in Chernobyl
(Ukraine) in 1986. Hay in Austria was contaminated by iodine 131 (half-life 8 days). If it is safe to feed the
cows the hay when only 10% of the iodine 131 remains, how long did the farmers need to wait to use this
hay?