Exponential Functions Word Problems

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = 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 quantity to grow exponentially?

Back

A quantity grows exponentially when it increases by a fixed percentage over equal time intervals.

Front

What does it mean for a quantity to decay exponentially?

Back

A quantity decays exponentially when it decreases by a fixed percentage over equal time intervals.

Front

What is the initial value in an exponential function?

Back

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

Front

How do you find the growth rate in an exponential growth problem?

Back

The growth rate is found by subtracting 1 from the base 'b' in the equation y = a(b)^x, expressed as a decimal.

Front

How do you find the decay rate in an exponential decay problem?

Back

The decay rate is found by subtracting the decay factor from 1, where the decay factor is the base 'b' in the equation y = a(b)^x.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^x, where 'r' is the growth rate.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^x, where 'r' is the decay rate.

Front

If a printer depreciates at a rate of 5%, what is the decay factor?

Back

The decay factor is 0.95, calculated as 1 - 0.05.

Front

If a dresser appreciates at a rate of 6%, what is the growth factor?

Back

The growth factor is 1.06, calculated as 1 + 0.06.