Logarithmic Functions and Their Applications

This video tutorial covers solving logarithmic word problems, similar to exponential problems but without a universal formula. It includes examples using box office revenues from Finding Nemo and Terminator 3, and a sound decibel level problem. The video explains how to set up and solve logarithmic equations, emphasizing the limited domain of logarithms and the importance of interpreting results in context.

What is the main difference between solving logarithmic and exponential word problems?

• Exponential problems require logarithms.

• Logarithmic problems do not have a universal formula.

• Exponential problems are more complex.

• Logarithmic problems have a catch-all formula.

In the Finding Nemo example, what does R(x) represent?

• The logarithmic base used in the equation.

• The derivative of the revenue function.

• The cumulative box-office revenue in millions.

• The number of weeks since the movie opened.

What is the first step in solving the Finding Nemo logarithmic equation?

• Divide by 78.05.

• Subtract 114.3 from both sides.

• Add 1 to both sides.

• Exponentiate both sides.

How many weeks after opening did Finding Nemo reach $300 million in revenue?

• 8.5 weeks

• 11.3 weeks

• 9.8 weeks

• 10.2 weeks

What is the logarithmic function used to model Terminator 3's revenue?

• R(x) = 78.05 * ln(x + 1) + 114.3

• R(x) = 26.203 * ln(x) + 90.798

• R(x) = 10 * log(x) + 75

• R(x) = 50 * ln(x + 2) + 100

What is the first step in solving the Terminator 3 logarithmic equation?

• Subtract 90.798 from both sides.

• Divide by 26.203.

• Exponentiate both sides.

• Add 1 to both sides.

How many weeks after opening did Terminator 3 reach $140 million in revenue?

• 8.5 weeks

• 7.5 weeks

• 6.5 weeks

• 5.5 weeks

What is the formula used to express decibel levels in terms of power levels?

• D = 10 * log(P1 / P2)

• D = 20 * log(P1 / P2)

• D = 10 * ln(P1 / P2)

• D = 20 * ln(P1 / P2)

If P2 is 75 watts, what is the value of P1 when D is 0.7 decibels?

• 92.12 watts

• 90.12 watts

• 88.12 watts

• 85.12 watts

What is the first step in solving the decibel level equation for P1?

• Divide both sides by 10.

• Multiply both sides by 75.

• Exponentiate both sides.

• Subtract 75 from both sides.