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 initial value in an exponential function represent?

Back

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

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 when b > 1, indicating how much the function increases.

Front

What is the decay factor in an exponential function?

Back

The decay factor is the base 'b' in the function f(x) = a(b)^x when 0 < b < 1, indicating how much the function decreases.

Front

How do you identify the asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function f(x) = a(b)^x is typically y = 0, as the function approaches this line but never touches it.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a quantity doubles every period, what is the growth factor?

Back

The growth factor is 2, as the quantity increases by a factor of 2 each period.

Front

If a quantity halves every period, what is the decay factor?

Back

The decay factor is 0.5, as the quantity decreases to half its value each period.

Front

How do you convert a percentage increase to a growth factor?

Back

To convert a percentage increase 'p%' to a growth factor, use the formula: growth factor = 1 + (p/100).