Exponential Functions Review

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

Front

What does the notation f(2) mean in a function?

Back

It means to evaluate the function f at x = 2.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the value of the function when x = 0, which is represented by the constant 'a' in the function f(x) = a * b^x.

Front

How do you interpret d(8) = 300 in the context of a function d(x)?

Back

It means that with 8 gallons of gas, the car can travel 300 miles.

Front

What does the equation y = 64(1/2)^x represent in a tournament context?

Back

It represents the number of teams remaining after x rounds, starting with 64 teams and halving the number each round.

Front

What is the initial value in the function f(x) = 2(4)^x?

Back

The initial value (y-intercept) is 2, which is the value of f(0).

Front

If h(t) = height of a plant after t weeks, what does h(4) = 5 mean?

Back

It means that after 4 weeks, the plant is 5 inches tall.

Front

What is the general form of an exponential decay function?

Back

An exponential decay function can be expressed as f(x) = a * (1 - r)^x, where 'r' is the decay rate.

Front

How do you find the value of a function at a specific point?

Back

Substitute the specific value into the function's equation.

Front

What does it mean if a function is increasing exponentially?

Back

It means that as x increases, the value of the function grows rapidly, typically doubling or increasing by a constant factor.