Exponential/Logarithmic Review

Front

What is the formula for compound interest?

Back

The formula for compound interest is 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 deposit), 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 is the value of log₄(64)?

Back

x = 3, because 4^3 = 64.

Front

What type of function is f(x) = 2(1/7)^x?

Back

Exponential Decay, because the base (1/7) is less than 1.

Front

If 3^3 = 3^(4x + 2), what is x?

Back

x = 1/4.

Front

What is the relationship between exponential functions and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y).

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.718.

Front

How do you solve for x in the equation (-3)^x = (-3)^13?

Back

Since the bases are the same, set the exponents equal: x = 13.

Front

What is the definition of 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 b ≠ 1.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

Front

What is the formula for converting between logarithmic and exponential forms?

Back

If log_b(a) = c, then it can be rewritten in exponential form as b^c = a.