Review for exponential exam!

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the rate of growth (as a decimal), and 'x' is the time period.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that adds the same value each time, represented by the equation f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

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

Back

Future Value = Present Value * (1 + r)^t, where 'r' is the growth rate and 't' is the number of time periods.

Front

What is the difference between linear and exponential growth?

Back

Linear growth adds a constant amount over time, while exponential growth multiplies by a constant factor, leading to faster increases as time progresses.

Front

If a car is worth $29,000 and increases by 10% each year, what will it be worth in 5 years?

Back

$46,704.79

Front

What is the formula for exponential decay?

Back

Exponential decay can be represented 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

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 does the term 'rate of growth' refer to in exponential functions?

Back

The rate of growth is the percentage increase applied to the initial value in each time period, expressed as a decimal.

Front

What is the graphical representation of an exponential function?

Back

The graph of an exponential function is a curve that rises rapidly, showing a steep increase as 'x' increases.

Front

What is a common real-world example of exponential growth?

Back

Population growth, where the number of individuals increases at a rate proportional to the current population size.