Write and Evaluate Exponential Functions

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 is the half-life of a substance?

Back

The half-life of a substance is the time required for half of the substance to decay or be eliminated from a system.

Front

How do you calculate the remaining amount of a substance after a certain time using half-life?

Back

Use the formula: Remaining Amount = Initial Amount * (1/2)^(time elapsed / half-life).

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'k' is the growth rate, and 't' is time.

Front

How do you model a population that triples every 20 minutes?

Back

Use the function y = 800 * 3^x, where 'y' is the population, '800' is the initial population, and 'x' is the number of 20-minute periods.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

If an investment doubles every 7 years, what is the growth function?

Back

The growth function is f(x) = P * 2^(x/7), where 'P' is the initial investment and 'x' is the number of years.

Front

How do you find the total amount after a certain number of years with exponential growth?

Back

Substitute the number of years into the growth function to find the total amount.

Front

What is the value of a population after 3 hours if it triples every 20 minutes starting from 800?

Back

After 3 hours (9 periods of 20 minutes), the population is 800 * 3^9 = 15,746,400.

Front

What does it mean for a function to be linear?

Back

A linear function has a constant rate of change and can be represented by the equation y = mx + b, where 'm' is the slope.