Unit 6: Flashcardziz #2 -Writing Exponential Functions

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.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a(b^x) where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a(b^x) where a > 0 and 0 < b < 1.

Front

How do you identify the starting amount in an exponential function?

Back

The starting amount is represented by the constant 'a' in the function f(x) = a(b^x).

Front

What does the exponent 'x' represent in an exponential function?

Back

The exponent 'x' represents the number of time intervals (e.g., years, months) that have passed.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers (y > 0) for growth functions and all positive real numbers (y < 0) for decay functions.

Front

How do you write an exponential function from a table of values?

Back

To write an exponential function from a table, identify the starting amount and the growth/decay factor, then use the form f(x) = a(b^x).

Front

What is the significance of the value '3000' in the function F(x) = 3000(1.035)^x?

Back

The value '3000' represents the starting amount or initial balance in the context of the function.

Front

What does the term 'growth rate' refer to in an exponential function?

Back

The growth rate is represented by the base 'b' in the function f(x) = a(b^x) and indicates how quickly the function increases.