Practice Flashcard 3.1-3.2 Ac Pre calc

Front

What is the half-life of a substance?

Back

The half-life of a substance is the time required for half of the substance to decay or be transformed into another substance.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = y0 * (1/2)^(t/h), where y0 is the initial quantity, t is time, and h is the half-life.

Front

What does the variable 'y' represent in the equation y = 20 (1/2)^(t/14)?

Back

In this equation, 'y' represents the mass of plutonium remaining after 't' years.

Front

How do you find the initial mass in an exponential decay equation?

Back

The initial mass is the value of 'y' when t = 0. In the equation y = 20 (1/2)^(t/14), the initial mass is 20 grams.

Front

How do you calculate the remaining mass after a certain number of years using the half-life?

Back

Substitute the number of years into the equation y = y0 * (1/2)^(t/h) to find the remaining mass.

Front

What is the value of y after 140 years if the half-life is 14 years?

Back

After 140 years, y = 20 * (1/2)^(140/14) = 0.0195 grams.

Front

What is the logarithmic property used to solve log equations?

Back

If log_b(A) = log_b(B), then A = B.

Front

Solve for x: log_4(3x-1) = log_4(2x+3).

Back

x = 4.

Front

What is the simplified form of e^(ln(x))?

Back

e^(ln(x)) = x.

Front

What is the simplified form of log_4(4^(3x))?

Back

log_4(4^(3x)) = 3x.