Introduction to Exponential Functions
What is the definition of an exponential function?
An exponential function is a mathematical function in which the variable appears in the exponent
Is the answer to ³√(4²) = 4^(3/2)
No, the correct answer is 4^(2/3)
Simplify the following expression:
√48
4√3
The value of a smartphone depreciates at a rate of 15% per year. If the initial value is $1,000, find the smartphone's value after 3 years.
614.13
Find the Domain and Range of f(x)=5^(x)
Domain: ARN
Range: y>0
Write the general notation for an exponential function.
The general notation for an exponential function is f(x) = a * b^x, where a is the initial value, b is the base, and x is the input variable.
What is the solution of 3^(x/2) * 3^(x/3) = 3^9
Write using rational exponents
√15
15^(1/2)
The value of a computer depreciates at a rate of 8% per year. If the initial value is $2,500, find the computer's value after 7 years.
1394.62
Find the Asymptote and y-intercept of f(x)=6^(x) -5
Asymptote: y = -5
y-intercept: (0,-4)
Why can't b in a exponential function be 1?
if b = 1, then b^x is always 1 and a horizontal line.
Solve the exponential equation: 3^(2x) = 27.
x=3/2
Simplify this expression:
√(3⁵ * 7⁴)
441√3
The population of rabbits doubles every 6 months. If there are initially 100 rabbits, how many will there be after 2 years? Applications of Exponential Growth and Decay
1600
Find the Domain and Range f(x)=3^(x)+5
Domain: ARN
Range: y > 5
Name two properties of exponential functions.
1) The domain is all real numbers. 2) The range is either positive or negative, depending on the graph
Solve the exponential equation:
81^(x+2) = 729^(2x+3)
x = -5/4
Simplify the expression below:
cube root √45 * cube root √(-75)
15 times cube root √-1
The population of a city is currently 500,000, and it is growing exponentially at a rate of 3% per year. Estimate the population after 20 years.
903,055
Find the Domain, range, asymptote, and y-intercept of f(x)=-3^(x) -5
Domain: ARN
Range: y > -5
Asymptote: y = -5
y intercept = (0,-4)
Give an example of an application of exponential functions.
One example of an application of exponential functions is compound interest, where the amount of money in an investment grows exponentially over time.
Solve this equation below:
16^(x+2) = 4^(x+5)
x = 1
Simplify the following expressions:
4√(6x²) * 3√(10x⁴)
24x³√15
Medication has a half-life of 6 hours. If a patient is given a 200 mg dose, how much will remain in their system after 24 hours?
(half life is when half of what's present dies at each interval.)
12.5
What is the asymptote, domain, range, and y-intercept of the function below?
f(x) = 5(6)^(x-2)
Domain: ARN
Range: y > 0
y-intercept: (0, 0.13889)