Exponential STAAR 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 the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for a population to be decreasing?

Back

A decreasing population means that the number of individuals in a population is declining over time, often represented by a function with a base less than 1.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the starting amount in an exponential function?

Back

The starting amount in an exponential function is the value of 'a' in the function f(x) = a(b)^x, representing the initial quantity before growth or decay.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, represented by a function with a base greater than 1.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over time, represented by a function with a base less than 1.

Front

How do you identify exponential growth or decay from a function?

Back

If the base of the function is greater than 1, it represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the decay rate in the function f(x) = 40(0.95)^x?

Back

The decay rate is 5%, as indicated by the base 0.95 (1 - 0.05 = 0.95).

Front

What does the term 'initial value' refer to in exponential functions?

Back

The initial value refers to the starting amount of the quantity being modeled, represented by 'a' in the function f(x) = a(b)^x.