Exponents and 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 a positive real number, and 'x' is the exponent.

Front

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

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, typically represented by a function of the form f(x) = a(b^x) where 0 < b < 1.

Front

How do you determine the initial value in an exponential function?

Back

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

Front

If a quantity decreases by 30% each hour, what is the remaining percentage after one hour?

Back

70% of the original quantity remains after one hour.

Front

What is the formula to calculate the remaining amount after exponential decay?

Back

The remaining amount can be calculated using the formula A = P(1 - r)^t, where P is the initial amount, r is the decay rate, and t is the time.

Front

What is the value of 'x' in the equation y = 75(1.2)^x for the year 2005 if the base year is 1998?

Back

x = 7, since 2005 - 1998 = 7.

Front

How do you simplify the expression m^7/n^2?

Back

The expression m^7/n^2 is already in its simplest form.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; if the base is greater than 1, the function represents growth, and if it is between 0 and 1, it represents decay.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x) where 0 < b < 1.

Front

How do you calculate the amount of a substance remaining after multiple hours of decay?

Back

Use the formula A = P(1 - r)^t, substituting P for the initial amount, r for the decay rate, and t for the number of hours.