Exponential Inequalities and Functions

The video tutorial explains how to solve an exponential inequality related to the number of leaves a tree has after X months. It involves isolating the variable x by removing the coefficient of 25 through division, followed by a long division process to simplify the equation. The tutorial then explores different powers of six to find the correct value that satisfies the inequality, concluding that 6 to the power of 3 is less than 216, making x equal to 3.

What is the context of the exponential inequality problem discussed in the video?

• The decay of a radioactive substance

• The population growth of a city

• The number of leaves a tree has over time

• The growth of bacteria in a petri dish

What is the first step in solving the given inequality?

• Add 25 to both sides

• Subtract 25 from both sides

• Multiply both sides by 25

• Divide both sides by 25

Why is long division used in the process of solving the inequality?

• To simplify the large number 5400

• To subtract the numbers

• To multiply the numbers

• To add the numbers

What is the result of dividing 5400 by 25?

• 25

• 216

• 150

• 54

After simplifying, what is the new form of the inequality?

• 6^x > 216

• 6^x ≥ 216

• 6^x = 216

• 6^x < 216

What is the value of x that satisfies the inequality 6^x < 216?

• 5

• 4

• 3

• 2

What is the power of 6 that equals 216?

• 6^2

• 6^3

• 6^4

• 6^5

Which inequality symbol correctly represents the solution to the problem?

• x < 3

• x > 3

• x ≥ 3

• x = 3

What is the final conclusion about the value of x in the inequality?

• x is greater than 3

• x is equal to 3

• x is less than 3

• x is greater than or equal to 3

What does the inequality 6^x < 216 represent in the context of the problem?

• The maximum number of leaves a tree can have

• The minimum number of leaves a tree can have

• The number of months it takes for a tree to reach 216 leaves

• The number of months it takes for a tree to have fewer than 216 leaves