PC Chapter 3 Review for Test

Front

What is the property of logarithms that states \( \ln(a) + \ln(b) = \ln(ab) \)?

Back

This property allows us to combine logarithms by multiplying their arguments.

Front

Solve for \( x \): \( \ln(x) + \ln(x - 4) = \ln(12) \)

Back

\( x = 6 \)

Front

What is the general form of an exponential decay function?

Back

The general form is \( N(t) = N_0 e^{kt} \), where \( N_0 \) is the initial amount, \( k \) is the decay constant, and \( t \) is time.

Front

If a radioactive substance has a decay constant of \( k = -0.4 \), how do you calculate the remaining amount after a certain time?

Back

Use the formula \( N(t) = N_0 e^{kt} \) to find the remaining amount.

Front

Calculate the remaining grams of a substance after 10 days if the initial amount is 86 grams and \( k = -0.4 \).

Back

\( N(10) = 86 e^{-0.4 \cdot 10} \approx 1.6g \)

Front

What is the formula for exponential growth?

Back

The formula is \( N(t) = N_0 e^{rt} \), where \( r \) is the growth rate.

Front

In a population growth model, if the initial population is 10,000 and the growth rate is 9% per year, how do you predict the population after 5 years?

Back

Use the formula \( N(t) = N_0 e^{rt} \) with \( r = 0.09 \) and \( t = 5 \).

Front

Predict the bird population in 2013 if it was 10,000 in 2008 with a growth rate of 9%.

Back

The predicted population is approximately 15,386.

Front

What does the graph of \( f(x) = \log_2(x + 2) \) look like?

Back

The graph is a logarithmic curve that increases slowly and has a vertical asymptote at \( x = -2 \).

Front

What is the base of the logarithm in the function \( f(x) = \log_2(x + 2) \)?

Back

The base is 2.