Math 2F Flashcard 2

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 is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function intersects the y-axis, which occurs when x = 0.

Front

How do you determine the y-intercept of the function y = 3^x?

Back

To find the y-intercept, substitute x = 0 into the equation: y = 3^0 = 1. Thus, the y-intercept is (0, 1).

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is P(t) = P0 * e^(rt), where P0 is the initial amount, r is the growth rate, and t is time.

Front

If a population grows at a rate of 25% per month, what is the growth factor?

Back

The growth factor for a 25% growth rate is 1 + 0.25 = 1.25.

Front

How do you calculate the population after a certain number of months with exponential growth?

Back

To calculate the population after a certain number of months, use the formula P = P0 * (growth factor)^n, where n is the number of months.

Front

What is the initial population in the mosquito problem?

Back

The initial population of mosquitoes at the beginning of the summer is 4,000.

Front

How many mosquitoes will there be after 4 months if the population grows at 25% per month?

Back

After 4 months, the population will be approximately 9,765 mosquitoes.

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if there are two or more outputs (y-values) for the same input (x-value).