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 function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal intervals of time, represented by a base greater than 1 in the function.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal intervals of time, represented by a base between 0 and 1 in the function.

Front

How do you write an expression for exponential growth?

Back

An expression for exponential growth can be written as y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

How do you write an expression for exponential decay?

Back

An expression for exponential decay can be written as y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be expressed as a_n = a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.

Front

What is the difference between a geometric sequence and an arithmetic sequence?

Back

A geometric sequence has a constant ratio between consecutive terms, while an arithmetic sequence has a constant difference between consecutive terms.

Front

How do you determine if a function is exponential growth or decay based on its base?

Back

If the base 'b' is greater than 1, the function represents exponential growth. If the base 'b' is between 0 and 1, it represents exponential decay.

Front

What is the initial value in an exponential function?

Back

The initial value in an exponential function is the value of the function when x = 0, represented by 'a' in the function f(x) = a * b^x.

Front

How do you express a 35% increase in an exponential function?

Back

A 35% increase can be expressed as y = a(1.35)^t, where 'a' is the initial amount and 't' is time.