Exponential Function Flashcard

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 have a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

How do you write an exponential decay function?

Back

An exponential decay function can be written as f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the value of the horizontal asymptote for the function y = a(b)^x when 0 < b < 1?

Back

The horizontal asymptote is y = 0.

Front

If a bacteria culture starts with 5000 cells and dies by 30% each year, what is the decay factor?

Back

The decay factor is 0.7.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function between two points is calculated as (f(b) - f(a)) / (b - a), where a and b are the x-values of the two points.

Front

How do you determine the balance of an investment after a certain number of years with compound interest?

Back

You can determine the balance by using the compound interest formula A = P(1 + r/n)^(nt).

Front

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

Back

The base 'b' determines the rate of growth or decay; if b > 1, the function represents growth, and if 0 < b < 1, it represents decay.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if its output values fall as the input values increase.