Topic 5B Review: Exponential Modeling

Front

What is exponential growth?

Back

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

Front

Define the formula for exponential growth.

Back

The formula for exponential growth is: N(t) = N0 * e^(rt), where N(t) is the quantity at time t, N0 is the initial quantity, r is the growth rate, and e is the base of the natural logarithm.

Front

What is the significance of the base 'e' in exponential functions?

Back

The base 'e' (approximately 2.718) is a mathematical constant that is the limit of (1 + 1/n)^n as n approaches infinity, and it is used in continuous growth models.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often the line y = 0.

Front

How do you calculate the future value of an investment with exponential growth?

Back

Use the formula: Future Value = Present Value * (1 + r)^t, where r is the growth rate and t is the time in periods.

Front

What happens to the value of an exponential function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential function with a positive base grows without bound, approaching infinity.

Front

What happens to the value of an exponential function as x approaches negative infinity?

Back

As x approaches negative infinity, the value of an exponential function approaches zero.

Front

What is the asymptote of the function y = 2^x?

Back

The asymptote of the function y = 2^x is y = 0.

Front

What is the asymptote of the function y = 2^x - 3?

Back

The asymptote of the function y = 2^x - 3 is y = -3.

Front

How do you determine the growth rate from a word problem?

Back

Identify the percentage increase per time period mentioned in the problem; this is your growth rate.