Transcript Section 4.2 Logarithms and Exponential Models

Section 4.2
Logarithms and Exponential Models
• The half-life of a substance is the amount of
time it takes for a decreasing exponential
function to decay to half of its initial value
• The half-life of iodine-123 is about 13 hours.
You begin with 100 grams of iodine-123.
– Write an equation that gives the amount of iodine
remaining after t hours
• Hint: You need to find your rate using the half-life
information
– Determine the number of hours for your sample to
decay to 10 grams
• Doubling time is the amount of time it takes
for an increasing exponential function to grow
to twice its previous level
• Suppose we put $1000 in an account paying
6.5% compounded annually
– Write an equation for the balance B after t years
– When will the amount in our account double?
• Any exponential function can be written as
Q = abt or Q = aekt
– Then b = ekt so k = lnb
• Convert the function Q = 5(1.2)t into the form
Q = aekt
– What is the annual growth rate?
– What is the continuous growth rate?
• Convert the function Q = 10(0.81)t into the
form Q = aekt
– What is the annual decay rate?
– What is the continuous decay rate?
• In your groups try problems 7, 10, and 32