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Questions and Answers
What is the approximate population of Southern right whales after 25 more years if the current population is 38 and it doubles over a 9-year period?
What is the approximate population of Southern right whales after 25 more years if the current population is 38 and it doubles over a 9-year period?
- 76
- 114
- 190
- 152 (correct)
A weight loss program targets a 10% weight loss each week.
A weight loss program targets a 10% weight loss each week.
False (B)
How many bacteria will be present after 2 hours if the culture starts with 20 individuals and doubles every 15 minutes?
How many bacteria will be present after 2 hours if the culture starts with 20 individuals and doubles every 15 minutes?
1280
The half-life of Carbon-14 is approximately _______ years.
The half-life of Carbon-14 is approximately _______ years.
Match the following weight loss goals with their corresponding time period:
Match the following weight loss goals with their corresponding time period:
In what year should the population of a developing city, starting at 125,000 in 2005 and growing at 8% per year, reach half a million?
In what year should the population of a developing city, starting at 125,000 in 2005 and growing at 8% per year, reach half a million?
A bacteria culture doubles every 30 minutes.
A bacteria culture doubles every 30 minutes.
What is the expected population of a city in 2020 if it grows by 8% yearly starting from 125,000 in 2005?
What is the expected population of a city in 2020 if it grows by 8% yearly starting from 125,000 in 2005?
What is the vertical transformation of the function $y = 1.5^x$ when represented as $y = -2(1.5)^x$?
What is the vertical transformation of the function $y = 1.5^x$ when represented as $y = -2(1.5)^x$?
The graph of $y = 1.5^x$ passes through the point (0, 1).
The graph of $y = 1.5^x$ passes through the point (0, 1).
What is the base of the exponential function in $y = 1.5^x$?
What is the base of the exponential function in $y = 1.5^x$?
In the transformed function $y = -2(1.5)^x$, the coefficient of _____ indicates vertical stretch.
In the transformed function $y = -2(1.5)^x$, the coefficient of _____ indicates vertical stretch.
Match the following properties of the functions:
Match the following properties of the functions:
How much of a radioactive isotope must technicians start with if they need at least 6 grams after 12 minutes and the half-life is 4 minutes?
How much of a radioactive isotope must technicians start with if they need at least 6 grams after 12 minutes and the half-life is 4 minutes?
It will take 15 years for there to be 1 tonne of radioactive waste remaining from a 100-tonne stockpile with a half-life of 15 years.
It will take 15 years for there to be 1 tonne of radioactive waste remaining from a 100-tonne stockpile with a half-life of 15 years.
How much of the initial population of Canada will remain after 50 years if it decreases by 0.5% per year starting from 34,482,779?
How much of the initial population of Canada will remain after 50 years if it decreases by 0.5% per year starting from 34,482,779?
A diver can see ____% of light after diving 60 meters, if the light is halved every 11 meters.
A diver can see ____% of light after diving 60 meters, if the light is halved every 11 meters.
Match the following radioactive decay examples with their given half-lives:
Match the following radioactive decay examples with their given half-lives:
What will the value of a $1000 investment grow to after 4 years at a growth rate of 2.5% per year?
What will the value of a $1000 investment grow to after 4 years at a growth rate of 2.5% per year?
What will Opa's pension be worth in 10 years if it increases by 6% annually starting from $24,300?
What will Opa's pension be worth in 10 years if it increases by 6% annually starting from $24,300?
After 1000 years, approximately 30 kg of a 40 kg Lead-210 sample remains.
After 1000 years, approximately 30 kg of a 40 kg Lead-210 sample remains.
An investment with a 2.4% annual return will double your money in 10 years.
An investment with a 2.4% annual return will double your money in 10 years.
How much should you invest now to ensure you have $2000 after 10 years at an interest rate of 2.4%?
How much should you invest now to ensure you have $2000 after 10 years at an interest rate of 2.4%?
What percentage of light remains at a depth of 60 meters if it is halved every 11 meters?
What percentage of light remains at a depth of 60 meters if it is halved every 11 meters?
Jeremiah's investment account will yield ______ when he turns 25, considering an annual interest rate of 8% compounded semi-annually.
Jeremiah's investment account will yield ______ when he turns 25, considering an annual interest rate of 8% compounded semi-annually.
Match the following terms to their definitions:
Match the following terms to their definitions:
Which function is decreasing?
Which function is decreasing?
The expression $y = 2(2)^x + 3$ represents a decreasing function.
The expression $y = 2(2)^x + 3$ represents a decreasing function.
The annual interest rate of Jeremiah's investment account is _____%.
The annual interest rate of Jeremiah's investment account is _____%.
What is the value of $g(x)$ if it is defined as $g(x) = -3(4)$?
What is the value of $g(x)$ if it is defined as $g(x) = -3(4)$?
The function $h(x) = -5(!)$ models a negative exponential graph.
The function $h(x) = -5(!)$ models a negative exponential graph.
What is the expected weight of the item mentioned as 12.5 grams?
What is the expected weight of the item mentioned as 12.5 grams?
The function $f(x) = 5(!)$ represents an exponential function with a base of ______.
The function $f(x) = 5(!)$ represents an exponential function with a base of ______.
Match the following values with their respective categories:
Match the following values with their respective categories:
Which of the following is a possible value for $b(x)$ defined as $b(x) = 3(4)$?
Which of the following is a possible value for $b(x)$ defined as $b(x) = 3(4)$?
The function $h(x) = -5(!)$ ensures the graph is always positive.
The function $h(x) = -5(!)$ ensures the graph is always positive.
How many kilograms does the item weigh if $0.85$ kg is mentioned?
How many kilograms does the item weigh if $0.85$ kg is mentioned?
Which function represents the steepest increasing graph?
Which function represents the steepest increasing graph?
The function g(x) = 25x is equivalent to r(x) = 52x.
The function g(x) = 25x is equivalent to r(x) = 52x.
What is the general shape of the graph of increasing exponential functions?
What is the general shape of the graph of increasing exponential functions?
The function ____ represents a decreasing exponential graph.
The function ____ represents a decreasing exponential graph.
Match the following functions with their equivalent forms:
Match the following functions with their equivalent forms:
Which of the following pairs of functions are equivalent?
Which of the following pairs of functions are equivalent?
H(x) = 32x and b(x) = 25x are equivalent graphs.
H(x) = 32x and b(x) = 25x are equivalent graphs.
Identify whether the function z(x) = 10x is increasing or decreasing.
Identify whether the function z(x) = 10x is increasing or decreasing.
The function p(x) = ____x has a coefficient that necessitates finding its equivalent function.
The function p(x) = ____x has a coefficient that necessitates finding its equivalent function.
What can be inferred about the functions with lower coefficients?
What can be inferred about the functions with lower coefficients?
Flashcards
Population Doubling
Population Doubling
When a population increases to twice its original size over a specific period.
Exponential Growth
Exponential Growth
Growth that increases at a constantly accelerating rate, often described by a pattern of doubling or multiplying over time.
Exponential Decay
Exponential Decay
A decrease in quantity that occurs at a steadily decreasing rate, often described by a pattern of halving or dividing over time.
Half-Life
Half-Life
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Calculate Future Population
Calculate Future Population
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Calculate Time for Decay
Calculate Time for Decay
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Percentage Decrease
Percentage Decrease
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Percentage Increase
Percentage Increase
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Radioactive Decay
Radioactive Decay
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Calculate remaining isotope
Calculate remaining isotope
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Population Growth/Decline
Population Growth/Decline
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Percentage Change
Percentage Change
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Sunlight Attenuation
Sunlight Attenuation
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Interest Growth
Interest Growth
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Compound Interest
Compound Interest
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Principal Amount
Principal Amount
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Interest Rate
Interest Rate
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Growth Rate
Growth Rate
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Compounding Frequency
Compounding Frequency
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Future Value
Future Value
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Present Value
Present Value
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Time Period
Time Period
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Parent Function
Parent Function
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Transformation
Transformation
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Vertical Stretch
Vertical Stretch
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Vertical Reflection
Vertical Reflection
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Vertical Compression
Vertical Compression
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Exponential Function
Exponential Function
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Base of an Exponential Function
Base of an Exponential Function
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Exponent of an Exponential Function
Exponent of an Exponential Function
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Increasing Exponential Function
Increasing Exponential Function
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Decreasing Exponential Function
Decreasing Exponential Function
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Matching Exponential Graphs
Matching Exponential Graphs
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Sketching Exponential Graphs
Sketching Exponential Graphs
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Graphing Exponential Functions
Graphing Exponential Functions
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What does the base '2' represent in an exponential function?
What does the base '2' represent in an exponential function?
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What does the base '0.5' represent in an exponential function?
What does the base '0.5' represent in an exponential function?
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Negative exponent
Negative exponent
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How to determine if an exponential function represents growth or decay?
How to determine if an exponential function represents growth or decay?
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Identify the exponential function for the graph
Identify the exponential function for the graph
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Write the exponential function for a graph
Write the exponential function for a graph
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Study Notes
Exponential Growth and Decay
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Whale Population: A Southern right whale population doubled every 9 years. Starting with 38 individuals, the population after 25 more years would be approximately 260 whales.
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Bacterial Growth: A bacteria culture doubles every 15 minutes. With an initial population of 20, after 2 hours (120 minutes), the population would be 5120. To reach a population of 163 840 would take 195 minutes.
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Weight Loss Program: If Helene loses 5% of her weight each week, from an initial weight of 280 pounds, she will weigh approximately 151.3 pounds after 12 weeks.
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City Population Growth: A developing city's population increases by 8% annually. Beginning with 125,000 people in 2005, the population in 2020 is projected to be 260,838 and reach 500,000 people by 2027.
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Carbon-14 Decay: A fossil of Carbon-14 with an initial weight of 100 grams, and a half-life of 6,000 years, will weigh approximately 12.5 grams after 18,000 years
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Radioactive Isotope Decay: A radioactive isotope with a 4-minute half-life requires a starting amount of at least 48 grams to have at least 6 grams remaining after 12 minutes.
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Radioactive Waste: A nuclear power plant has 100 tonnes of radioactive waste with a 15-year half-life. It will take approximately 100 years to reduce the amount of waste to 1 tonne.
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Canada's Population: With a population decrease of 0.5% per year, Canada's current population of 34,482,779 would be approximately 26,838,379 in 50 years.
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Sunlight Penetration: Light penetration halves every 11 meters of depth. At 60 meters, only 2.28% of surface light would remain.
Interest
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Pension Growth: A pension increasing by 6% annually, starting from $24,300. It will be worth $43,517.60 in 10 years.
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Investment Growth: An investment of $1000 at a 2.5% annual growth rate for 4 years will be worth $1103.81 after that time.
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Investment Calculation: If you need $2000 after 10 years with an interest rate of 2.4%, the initial investment should be $1577.72.
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Compound Interest: Jeremiah's grandparents' $3,000 investment, at an 8% annual interest rate compounded semi-annually, will be worth around $21 320.05 when Jeremiah turns 25.
Exponential Functions (Graphs and Transformations)
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Graphing Exponential Functions: Transformations of parent exponential functions to create new functions.
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Graphing and Function Definition: Graphing increasing and decreasing exponential functions, along with the function definition.
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Determining Exponential Function: Finding the function of an exponential graph given the points and characteristics.
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Description
This quiz covers concepts related to exponential growth and decay, including population dynamics, bacterial growth, and transformations of exponential functions. Test your understanding of growth rates, half-lives, and how to model these scenarios mathematically.
