Interpreting Exponential Functions Using Function Notation Task

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 the base (a positive real number), and 'x' is the exponent. It describes growth or decay processes.

Front

What does the notation f(d) represent in the context of functions?

Back

f(d) represents the value of the function f at a specific input d. It indicates how the output of the function changes based on the input value.

Front

What is the initial value in an exponential function?

Back

The initial value is the value of the function when the input is zero, often represented as f(0). It indicates the starting point of the function.

Front

How do you interpret f(4.5) in the context of a flu epidemic?

Back

f(4.5) represents the number of people with the flu after 4.5 days since the epidemic began.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay factor. If the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

Front

How can you find the value of f(t) for a specific t in an exponential function?

Back

To find f(t), substitute the value of t into the function's equation and calculate the result.

Front

What does it mean if f(t) = 1500 in the context of a flu epidemic?

Back

It means that after a certain number of days, the number of people with the flu reached 1500.

Front

What is the significance of the coefficient in an exponential function?

Back

The coefficient (the constant 'a' in f(x) = a * b^x) represents the initial amount or starting value of the function.

Front

How do you determine the rate of growth in an exponential function?

Back

The rate of growth is determined by the base of the exponential function. For example, in f(d) = 50 * (3/2)^d, the growth rate is (3/2) per day.

Front

What does it mean for a function to be increasing exponentially?

Back

A function is increasing exponentially if its output values grow at an increasing rate as the input values increase.