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

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase that occurs when the growth rate of a value is proportional to its current value, leading to the value increasing rapidly over time.

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'exponential decay' mean?

Back

Exponential decay refers to a decrease that occurs when the decay rate of a value is proportional to its current value, leading to the value decreasing rapidly over time.

Tags

CCSS.HSF-IF.C.8B

Front

In the function y = a(1 + r)^t, what does 'r' represent?

Back

'r' represents the rate of growth or decay expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

Front

What is the y-intercept in 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).

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.

Front

What does the 'a' represent in the exponential function f(x) = a(b^x)?

Back

'a' represents the initial value or the y-intercept of the function.

Tags

CCSS.HSF.LE.B.5

Front

If a function has a base of less than 1, what type of function is it?

Back

It is an exponential decay function.

Tags

CCSS.HSF-IF.C.8B