PC - Sem 1 Review Unit 4 Exponential and Log Functionss

Front

What is the result of (2x^3y)^6?

Back

64x^18y^6

Front

What interest rate is needed to turn $500 into $750 in 5 years with continuous compounding?

Back

8.1%

Front

What is the vertical asymptote of the function f(x)=log_5(x+4) - 2?

Back

x = -4

Front

Expand ln(xy^2z^3).

Back

lnx + 2lny + 3lnz

Front

Solve log_8(4x+4)=2.

Back

x = 15

Front

What is the definition of an exponential function?

Back

A 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 definition of a logarithm?

Back

The logarithm log_b(a) is the exponent to which the base b must be raised to produce the number a.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the relationship between exponential and logarithmic functions?

Back

They are inverse functions; if y = b^x, then x = log_b(y).

Front

What is the formula for continuously compounded interest?

Back

A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.