7.1-7.2 Exponential Functions Worksheet

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 an investment to be compounded quarterly?

Back

Compounding quarterly means that the interest is calculated and added to the principal four times a year, resulting in interest being earned on previously accumulated interest.

Front

How do you calculate the future value of an investment using the formula FV = P(1 + r/n)^(nt)?

Back

FV is the future value, P is the principal amount, r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the value of e^0?

Back

The value of e^0 is 1, as any number raised to the power of 0 equals 1.

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What is the approximate value of e^-4?

Back

The approximate value of e^-4 is 0.0183.

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If you invest $850 at an annual interest rate of 2.3% for 8.5 years, what is the total amount?

Back

The total amount after 8.5 years is approximately $1,033.53.

Front

How do you find the amount in a savings account after a certain number of years with no additional deposits?

Back

Use the formula A = P(1 + r)^t, where A is the amount, P is the principal, r is the annual interest rate, and t is the time in years.

Front

What is the formula for continuous compounding?

Back

The formula for continuous compounding is A = Pe^(rt), where A is the amount, P is the principal, r is the annual interest rate, and t is the time in years.

Front

What is the significance of the number 'e' in exponential functions?

Back

The number 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models.

Front

How do you calculate the total amount for an investment compounded quarterly?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.