4.3 Exponential Compound Interest Practice/Review

Front

What is the formula for calculating compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

Front

What does 'compounded annually' mean?

Back

It means that the interest is calculated and added to the principal once per year.

Front

How do you determine the total amount in an account after a certain number of years with compound interest?

Back

You use the compound interest formula: A = P(1 + r/n)^(nt).

Front

What is the significance of the 'a' in an exponential function?

Back

The 'a' represents the y-intercept of the function, which is the value of the function when x = 0.

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical function of the form f(x) = a * b^x, where a > 0 and b > 1, indicating that the quantity increases rapidly as x increases.

Front

What is an exponential decay function?

Back

An exponential decay function is a mathematical function of the form f(x) = a * b^x, where a > 0 and 0 < b < 1, indicating that the quantity decreases rapidly as x increases.

Front

What is the horizontal asymptote of an exponential function?

Back

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

Front

How do you find the horizontal asymptote of the function f(x) = 3(2)^(x-4) + 5?

Back

The horizontal asymptote is y = 5, which is the constant added to the exponential part of the function.

Front

What is the effect of increasing the interest rate on the amount of compound interest earned?

Back

Increasing the interest rate will increase the amount of compound interest earned, leading to a higher total amount in the account.

Front

What is the effect of increasing the number of compounding periods per year?

Back

Increasing the number of compounding periods per year will result in more interest being calculated and added to the principal, leading to a higher total amount.