4.7 Applications Involving Exponential Functions.notebook

4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
2015 05 13
4.7 Applications Involving Exponential Functions
y=a(b)
initial value
x
ratio
The population of St. Thomas can be modeled by the , where P is the population equation and t is the time in years since 1980.
a. What is the growth rate (as a %)?
b. What is the current population of St. Thomas?
c. When will the population reach 40,000?
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4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
Ex. Mr. Mann has just purchased a new car worth $18,500. Every year from now on the car's value will decrease by 23% (this is known as depreciation). a. Determine an equation that will model this situation.
b. What will the value of the car be in 2022?
c. If Mr. Mann wants to sell the car when it's value drops below $3000, when will this occur?
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4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
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4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
Ex. A population of 360 bacteria will double once every 4 hours. a. Write an equation that will model this situation.
b. How many bacteria will there be after 1 day?
c. When will there be 10,000 bacterium?
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4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
A mug of coffee is placed on a counter to cool. The temperature (T) of the coffee oC, t minutes after it is put on the counter is modeled by the equation
a. What was the initial temperature of the coffee?
b. What is the temperature of the room?
c. Max wants to drink his coffee when it is 50oC, when can he start the coffee?
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4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
Ex. Radioactive isotopes decay at a regular rate. The Carbon‐
14 isotope is used in the process of Carbon Dating, because it has a long and predictable half‐life. That means that approximately every 5730 years, a sample containing carbon will lose half of it's carbon‐14 atoms. Scientists have been able to use this knowledge to approximate the age of fossils and other remains, which have helped to confirm some of the aspects of the theory of evolution. A spearhead is found today containing 80mg of Carbon‐14. The Mass of Carbon‐14 remaining can be modeled by the equation where, t is the time in years since the sample was found.
a. how much carbon‐14 will there be remaining in 3000 years?
b. The archaeologists who discovered the spearhead know that the sample would have initially contained approximately 280±15mg. How old is the fossil?
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4.7 Applications Involving Exponential Functions.notebook
May 13, 2015
The population of a colony of bacteria growing in a Petri dish can be modeled by the equation:
, where P is the population and t is the time in minutes.
a.
What is the initial population of the bacterial colony?
b.
What is the population of the colony 1 hour after the start of the experiment?
c.
When does the population reach 5000?
Pg. 261 #2,3,6,7,9,10,12,15,16
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