Calculating Exports and Logarithms

The video tutorial explains how to determine the year when China's automobile and parts exports will reach 8.2 billion dollars using an exponential equation. The process involves setting up the equation, isolating the exponential part, and using logarithms to solve for the time variable, T. The solution is calculated using a calculator, and the result is rounded to one decimal place. Finally, the year is determined by adding the calculated time to the base year, 1998, resulting in the year 2002.4.

What does the variable T represent in the context of the problem?

• The value of exports in billions

• The base of the natural logarithm

• The initial export value

• The number of years after 1998

What is the significance of the year 1998 in this problem?

• It is the year when the exports started

• It is the year when the equation was derived

• It is the year when exports reached 8.2 billion

• It is the base year for T

What is the first step in solving the equation for T?

• Divide both sides by 1.8415

• Multiply both sides by 1.8415

• Subtract 8.2 from both sides

• Add 1998 to both sides

After isolating the exponential part, what is the approximate value of the quotient?

• 1.6180

• 2.7182

• 4.4529

• 3.1415

Which mathematical operation is used to move T out of the exponent position?

• Multiplication

• Logarithm

• Subtraction

• Addition

What is the value of natural log E?

• Infinity

• 1

• 0

• E

What is the purpose of using a calculator in this problem?

• To add 1998 to T

• To find the initial export value

• To calculate the natural log

• To determine the value of E

What is the final calculated value of T?

• 6.8

• 3.2

• 4.4

• 5.6

In what year does the export value reach 8.2 billion dollars?

• 2002.4

• 2003.4

• 2000.4

• 2001.4

Why is it necessary to round the final answer to one decimal place?

• To comply with the problem's instructions

• To match the precision of the initial data

• To simplify the calculation

• To make the answer more accurate