Exponential Functions Practice

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 increasing exponentially?

Back

It means that the population grows by a constant percentage over equal time intervals, leading to rapid growth as time progresses.

Tags

CCSS.HSF-LE.A.1C

Front

What does it mean for a population to be decreasing exponentially?

Back

It means that the population decreases by a constant percentage over equal time intervals, leading to rapid decline as time progresses.

Tags

CCSS.HSF-IF.C.8B

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b^x). If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B

Front

In the function f(x) = 12(1.015)^t, what does the base 1.015 represent?

Back

The base 1.015 represents a growth factor of 1.5%, indicating that the population increases by 1.5% each year.

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, showing that the values of the function increase rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, showing that the values of the function decrease rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What does the expression f(x) = 2(0.85)^x represent?

Back

This expression represents exponential decay, as the base 0.85 is less than 1, indicating a decrease over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the value of the growth factor in f(x) = 10(0.3)^x?

Back

The growth factor is 0.3, indicating that the function represents exponential decay.

Tags

CCSS.HSF-IF.C.8B