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Pre-Calculus 12 Notes
By:
Gen L.
Lesson 6: Applications
Types of Applications
An exponential function is in the form
, where
is a constant and
.
There are two types we will consider.
Type I:
is a % (Compound Interest)
Type II: Growth and Decay (Double, Triple and Half-life)
Type I: Compound Interest
compounded annually or % increase.
compounded n times / year.
% decrease.
Note: We're only focusing on the discrete case.
Type I Example (Interest)
An investment of $500 is earning interest at 6% / annum (year) compounded semi-annually. How long until they double their investment ($1000)?
yrs.
Type I Example (Increase)
The population increases at a rate of 7% / year. Currently, there are 1250 people. How long until there is 5000 people?
yrs.
Type I Example (Decrease)
An awful investment decreases at a rate of 4% / year. If the original investment was worth $450, how long until it is worth $320?
yrs.
Type II: Growth / Decay
Doubling:
Tripling:
Half-Life:
Type II Example (Doubling)
The population of rabbits doubles every 3 months. If there are 12 rabbits now, how many months until there are 600 rabbits?
months
Type II Example (Tripling)
An insect colong triples every 20 weeks. If there are currently 1300 insects, how long until there are 6000 insects?
weeks.
Type II Example (Half-life)
Lead-210 is a radioactive nuclide. If its half-life is 20 years, how long will it take 300g to decay to 200g?
years.
Type II Example (Rates)
A radioactive substance decays from 10g to 5.6g in 5 years. What is its half-life?
years.
Type I Example (Optics)
The amount of visible light decreases by 5% / metre a diver descends below the surface. How many metres below is the diver when she sees 20% of the surface light?
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