Dog Age Calculations and Logarithms

The video tutorial explains how to relate a dog's age to a human's age using the equation y = 16 * ln(x) + 31, where x is the dog's age and y is the human age. It demonstrates calculating the human age for a 2-year-old dog, resulting in approximately 42.1 years, and finding the dog age for a 65-year-old human, which is about 8.4 years. The tutorial covers using natural logarithms and exponential equations to solve these problems, providing step-by-step instructions and rounding techniques.

What is the equation used to relate a dog's age to human years?

• y = 16 * ln(x) + 31

• y = 31 * ln(x) + 16

• y = 31 * x + 16

• y = 16 * x + 31

If a dog is 2 years old, what is its approximate age in human years?

• 35.5 years

• 42.1 years

• 31.2 years

• 40.0 years

What is the first step in calculating the human age for a 2-year-old dog?

• Multiply 16 by 2

• Find the natural log of 2

• Add 31 to 2

• Divide 16 by 2

Why do we round the result to the nearest tenth?

• To simplify the calculation

• To make it easier to read

• To match the precision of the input

• To provide a more accurate representation

What is the first step in solving for a dog's age if it is 65 in human years?

• Divide 65 by 16

• Subtract 31 from 65

• Add 31 to 65

• Multiply 65 by 16

After isolating the natural log of x, what is the next step?

• Convert to a logarithmic equation

• Convert to an exponential equation

• Add 31 to both sides

• Multiply both sides by 16

What is the base used when converting the logarithmic equation to exponential form?

• 2

• 10

• 16

• e

What is the approximate age of a dog in dog years if it is 65 in human years?

• 7.5 years

• 8.4 years

• 9.2 years

• 10.1 years

What is the common factor used to simplify 34/16?

• 2

• 3

• 4

• 5

What is the exponent in the exponential equation derived from the logarithmic form?

• 34/16

• 17/8

• 16

• 8