PC Chapter 3 Review for Test

PC Chapter 3 Review for Test

Assessment

Flashcard

Mathematics

9th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

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15 questions

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1.

FLASHCARD QUESTION

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.

2.

FLASHCARD QUESTION

Front

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

Back

\( x = 6 \)

3.

FLASHCARD QUESTION

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.

4.

FLASHCARD QUESTION

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.

5.

FLASHCARD QUESTION

Front

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

Back

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

6.

FLASHCARD QUESTION

Front

What is the formula for exponential growth?

Back

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

7.

FLASHCARD QUESTION

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 \( t = 5 \).

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