#1
What is the formula for exponential growth?
A = P(1 + r)^t
ExplanationExponential growth formula with initial amount, growth rate, and time.
#2
Which of the following represents exponential decay?
A = P(1 - r)^t
ExplanationExponential decay formula with initial amount, decay rate, and time.
#3
Which of the following best describes exponential growth?
Rapid increase over time
ExplanationCharacteristic description of exponential growth involving rapid increase.
#4
What does 'r' represent in the formula for exponential growth or decay?
Rate of growth or decay
ExplanationSymbolic representation of growth or decay rate in exponential formulas.
#5
Which of the following equations represents exponential growth?
y = a(1 + r)^x
ExplanationEquation depicting exponential growth with initial amount, growth rate, and time.
#6
What happens to the rate of decay as time increases in exponential decay?
It decreases
ExplanationCharacteristic of exponential decay where decay rate diminishes over time.
#7
If an investment grows at a rate of 5% annually, which equation represents its exponential growth?
A = P(1 + 0.05)^t
ExplanationExponential growth equation incorporating a 5% annual growth rate.
#8
The half-life of a substance is 10 years. What is its decay constant (rounded to two decimal places)?
0.069
ExplanationDecay constant derived from half-life, indicating rate of exponential decay.
#9
What is the general form of the exponential decay function?
y = a(1 - r)^x
ExplanationGeneral format of exponential decay function involving initial amount, decay rate, and time.
#10
If a radioactive substance has a half-life of 20 years, what fraction of the substance remains after 60 years?
1/8
ExplanationFraction of substance remaining calculated from its half-life over time.
#11
The population of a city is 10,000 and is decreasing at a rate of 2% per year. What will be the population after 10 years (rounded to the nearest integer)?
8200
ExplanationProjected population after 10 years using exponential decay formula.
#12
If an investment doubles in value every 5 years, what is the annual growth rate (rounded to the nearest integer)?
16%
ExplanationAnnual growth rate derived from the time it takes for an investment to double.
#13
In a population, if the growth rate is 2% per year and the initial population is 1000, what will be the population after 10 years (rounded to the nearest integer)?
1219
ExplanationPopulation growth calculated using exponential growth formula after 10 years.
#14
The population of a town is currently 5000 and is increasing at a rate of 3% per year. What will be the population after 5 years (rounded to the nearest integer)?
5761
ExplanationPopulation projection after 5 years using exponential growth formula.
#15
What is the time taken for an investment to triple in value if it grows at a rate of 6% per year?
Approximately 12.5 years
ExplanationTime duration required for an investment to triple based on its growth rate.
#16
The value of a car depreciates by 10% annually. If the initial value of the car is $20,000, what will be its value after 5 years (rounded to the nearest dollar)?
$12,960
ExplanationProjected value of the car after 5 years accounting for annual depreciation.
#17
If a radioactive substance has a half-life of 25 years, what fraction of the substance will remain after 50 years?
1/8
ExplanationFraction of substance remaining after 50 years based on its half-life.