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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?
A weight loss program targets a 10% weight loss each week.
A weight loss program targets a 10% weight loss each week.
False
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.
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Match the following weight loss goals with their corresponding time period:
Match the following weight loss goals with their corresponding time period:
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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?
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A bacteria culture doubles every 30 minutes.
A bacteria culture doubles every 30 minutes.
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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?
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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 $y = -2(1.5)^x$?
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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).
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What is the base of the exponential function in $y = 1.5^x$?
What is the base of the exponential function in $y = 1.5^x$?
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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.
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Match the following properties of the functions:
Match the following properties of the functions:
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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?
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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.
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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?
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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.
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Match the following radioactive decay examples with their given half-lives:
Match the following radioactive decay examples with their given half-lives:
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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?
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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?
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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.
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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.
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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%?
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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?
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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.
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Match the following terms to their definitions:
Match the following terms to their definitions:
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Which function is decreasing?
Which function is decreasing?
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The expression $y = 2(2)^x + 3$ represents a decreasing function.
The expression $y = 2(2)^x + 3$ represents a decreasing function.
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The annual interest rate of Jeremiah's investment account is _____%.
The annual interest rate of Jeremiah's investment account is _____%.
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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 $g(x) = -3(4)$?
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The function $h(x) = -5(!)$ models a negative exponential graph.
The function $h(x) = -5(!)$ models a negative exponential graph.
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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?
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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 ______.
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Match the following values with their respective categories:
Match the following values with their respective categories:
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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 $b(x) = 3(4)$?
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The function $h(x) = -5(!)$ ensures the graph is always positive.
The function $h(x) = -5(!)$ ensures the graph is always positive.
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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?
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Which function represents the steepest increasing graph?
Which function represents the steepest increasing graph?
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The function g(x) = 25x is equivalent to r(x) = 52x.
The function g(x) = 25x is equivalent to r(x) = 52x.
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What is the general shape of the graph of increasing exponential functions?
What is the general shape of the graph of increasing exponential functions?
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The function ____ represents a decreasing exponential graph.
The function ____ represents a decreasing exponential graph.
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Match the following functions with their equivalent forms:
Match the following functions with their equivalent forms:
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Which of the following pairs of functions are equivalent?
Which of the following pairs of functions are equivalent?
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H(x) = 32x and b(x) = 25x are equivalent graphs.
H(x) = 32x and b(x) = 25x are equivalent graphs.
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Identify whether the function z(x) = 10x is increasing or decreasing.
Identify whether the function z(x) = 10x is increasing or decreasing.
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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.
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What can be inferred about the functions with lower coefficients?
What can be inferred about the functions with lower coefficients?
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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.
