Chapter 6 Flashcards
What is the general form of an exponential function?
Y = ab*
What is the base in an exponential function?
b is called the base and must be a positive real number other than 1.
What characterizes an exponential growth function?
If b > 1, then y = ab* is an exponential growth function.
What is the growth factor in an exponential function?
b is called the growth factor.
What characterizes an exponential decay function?
If 0 < b < 1, then y = ab* is an exponential decay function.
What is the decay factor in an exponential function?
b is called the decay factor.
What is the asymptote in exponential growth?
The graph approaches the asymptote at Y=0 from above
The horizontal line Y=0 is the asymptote that the graph approaches but never touches.
How does the graph of exponential growth behave from left to right?
The graph is increasing
Exponential growth indicates that as the input increases, the output increases rapidly.
What is the domain of exponential growth?
The domain is R
This means all real numbers are valid inputs for the exponential function.
What is the range of exponential growth?
The range is (0, ∞)
This indicates that the output values are greater than zero but can extend to infinity.
What is the asymptote in exponential decay?
ysO
The asymptote represents a value that the graph approaches but never touches.
How does the graph of exponential decay behave?
The graph is decreasing from left to right.
What is the domain of exponential decay?
RR
The domain refers to all possible input values for the function.
What is the range of exponential decay?
(0, ∞)
The range indicates all possible output values of the function.
In exponential decay, what condition is true for y?
y > 0
What are Exponential Models used for?
To model quantities that increase or decrease by a fixed percent each year.
Exponential Models are commonly used in finance, biology, and many other fields to represent growth and decay processes.
What is the formula for the Exponential Growth Model?
y = a(1 + r)^t
In this formula, ‘y’ represents the final amount, ‘a’ is the initial amount, ‘r’ is the growth rate, and ‘t’ is the time in years.
In the Exponential Growth Model, what does ‘a’ represent?
Initial amount.
This is the starting value before any growth has occurred.
In the Exponential Growth Model, what does ‘1 + r’ represent?
Growth factor.
This factor indicates how much the quantity grows each year, based on the growth rate ‘r’.
What is the general form of the Exponential Decay Model?
y = a(1 - r)^t
Similar to growth, this model represents how quantities decrease over time.
In the Exponential Decay Model, what does ‘r’ represent?
Decay rate.
This represents the percentage decrease of the quantity each year.
In the Exponential Decay Model, what does ‘1 - r’ represent?
Decay factor.
This factor indicates how much the quantity decreases each year, based on the decay rate ‘r’.
Fill in the blank: The formula for the Exponential Growth Model is y = a(_______)^t.
(1 + r)
This indicates the growth factor applied to the initial amount over time.
True or False: The Exponential Growth Model can only be used for quantities that decrease over time.
False.
The Exponential Growth Model is specifically designed for quantities that increase over time.
What type of processes can Exponential Models represent?
Growth and decay processes.
These processes are found in various fields, including population dynamics and compound interest calculations.
What is the formula for Compound Interest?
A = P(1 + r/n)^(nt)
A = total amount, P = initial amount, r = interest rate, n = number of compounding periods, t = time
What does ‘A’ represent in the Compound Interest formula?
Total amount
A is the amount of money accumulated after n years, including interest.
What does ‘P’ stand for in the Compound Interest formula?
Initial amount
P is the principal amount or the initial sum of money.
What does ‘n’ denote in the Compound Interest formula?
Number of compounding periods
n indicates how often the interest is compounded within a year.
How many compounding periods are there if interest is compounded daily?
365
Daily compounding means interest is calculated and added to the principal every day.
How many compounding periods are there if interest is compounded monthly?
12
Monthly compounding means interest is calculated and added to the principal every month.
How many compounding periods are there if interest is compounded quarterly?
4
Quarterly compounding means interest is calculated and added to the principal every three months.
How many compounding periods are there if interest is compounded annually?
1
Annual compounding means interest is calculated and added to the principal once a year.
What does ‘r’ represent in the Compound Interest formula?
Rate
r is the annual interest rate expressed as a decimal.
What does ‘t’ represent in the Compound Interest formula?
Time
t is the time in years for which the money is invested or borrowed.
What does A represent in the compound interest formula?
Total amount
A is the final amount accumulated after interest is applied.
What does P represent in the compound interest formula?
Initial amount
P is the principal or starting amount before interest.
What is the formula for compound interest when compounding continuously?
A = Pert
This formula shows how the total amount A is calculated using the initial amount P, the rate r, and the time t.
In the formula A = Pert, what does ‘r’ stand for?
Rate
r is the interest rate expressed as a decimal.
In the formula A = Pert, what does ‘t’ stand for?
Time
t is the time period for which the money is invested or borrowed.
