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Calculating Exponential Decay
供稿人: Williams
(原作者: Potter)
Remember that there are two types of exponential functions:
Remember that the criteria for each type is . . . 
b > 1
Growth
Calculating Exponential Values
0< b < 1
Decay
Let's discuss          .
Remember that there are two types of exponential functions:
Remember that the criteria for growth is . . . 
0 < b < 1
Calculating Exponential Values
decay
y = a•(b)x
y = a•(       )x
The common form of the equation will be used for calculations:
The base, b will be expressed differently to make it more obviousthat it is less than 1 . . .
where "r" is the percent decrease.Also, these problems are time based so the variable "x" is replaced by "t".
So the modified equation looks like:
y = a•(       )
1-r
1-r
Calculating Exponential Values
t
Let's see if you can identify the numerical values given the terms:
Victor gets a truck for $17000. The value of the truck decreases by 4% each year.Find the value of the truck after 3 years.

The equation for the exponential function: y = 17000•(1-0.04)t or y = 17000•(0.96)t
Decay factor:(multiplier)
Overview of terminology for growth:
Initial amount: $
y = a•(       )
initial amount
1-r
Calculating Exponential Values
decay factor: a single value 1-r
t
Percent decrease:(as a percent)
What value will be put in for "t":
percent decrease
time
%
Let's see if you can calculate the value of the truck 3 years later.
Victor gets a truck for $17000. The value of the truck decreases by 4% each year.Find the value of the truck after 3 years.

The equation for the exponential function:
y = 17000•(1-0.04)t


y = $
y = a•(      )
1-r
Calculating Exponential Values
since we are calculating money and the amount is
large, round your answer to the nearest dollar.
t
Decay factor:(multiplier)
Round your answer to the nearest dollar.
A company purchased machinery in the year 1995 for $8800. Its cost depreciatedby 5% each year. What is the value of the machinery after 4 years?
Initial amount: $
Subtituting into the equation: y =
y = a•(      )
1-r
Calculating Exponential Values
t
What value will be put in for "t":
Percent decrease:(as a percent)
•(
Answer: $
%
)
Round your answer to the nearest dollar.
Ed takes a bike for $4600. The bike's value decreases by 12% each year.
What is the bike's value after 5 years?
y = a•(      )
1-r
Calculating Exponential Values
t
Answer: $
Round your answer to the nearest dollar.
Francis started a business in the year 1991. He got $13000 profit in the first year.Each year his profit decreased by 3%. What are his profits for the tax year 1997?
y = a•(      )
1-r
Calculating Exponential Values
t
Answer: $
Round your answer to the nearest dollar.
A business made a profit of $17000 in 1991. Then its profits decreased by 6% eachyear for 5 years. Find its profit in the year 1996.
y = a•(      )
1-r
Calculating Exponential Values
t
Answer: $
Round your answer to the nearest dollar.
A company purchased machinery in the year 1990 for $7000. Its cost deprecatedat a rate of 4% per year. What is the value of the machinery after 10 years?
y = a•(      )
1-r
Calculating Exponential Values
t
Answer: $
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