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.

Tags

CCSS.HSF.BF.B.5

Front

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

Back

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

Tags

CCSS.HSF-IF.C.8B

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).

Tags

CCSS.HSF.BF.B.5

Front

What is the base of the natural logarithm?

Back

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

Tags

CCSS.HSF.BF.B.5

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).

Tags

CCSS.HSF-IF.C.8B

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.

Tags

CCSS.HSF.BF.B.5