Understanding Obesity Rate Calculation

The video tutorial explains how to determine the year when the obesity rate in the U.S. was 19.7% using a mathematical model. The model is given by the function p(t) = 2.9√t + 12, where t is the number of years after 1982. By substituting 19.7 for p(t), the tutorial demonstrates how to solve for t, isolate the square root, and calculate the year. The solution involves subtracting, dividing, and squaring operations, leading to the conclusion that the year is approximately 1989.

What is the mathematical model used to represent the obesity rate of U.S. adults?

• p(t) = 3.5 * t + 10

• p(t) = 2.9 * sqrt(t) + 12

• p(t) = 2.9 * t^2 + 12

• p(t) = 3.5 * sqrt(t) + 10

In the given model, what does the variable 't' represent?

• The number of years after 1990

• The number of years after 1982

• The number of years after 1980

• The number of years after 2000

What value is substituted for p(t) to find the year when the obesity rate was 19.7%?

• 7.7

• 19.7

• 12

• 2.9

What is the first step in isolating the square root in the equation?

• Add 12 to both sides

• Multiply both sides by 2.9

• Divide both sides by 2.9

• Subtract 12 from both sides

After isolating the square root, what operation is performed next?

• Multiply both sides by 2.9

• Subtract 12 from both sides

• Square both sides

• Add 12 to both sides

What is the approximate value of t after solving the equation?

• 7.05

• 6.05

• 9.05

• 8.05

To the nearest year, what is the value of t?

• 9

• 8

• 7

• 6

What year corresponds to t = 7 in the context of the problem?

• 1990

• 1989

• 1988

• 1987

What is the significance of the year 1989 in this problem?

• It is the year the obesity rate was 2.9%.

• It is the year the obesity rate was 12%.

• It is the year the obesity rate was 19.7%.

• It is the year the model was created.

What is the final step in determining the year when the obesity rate was 19.7%?

• Multiplying t by 1982

• Dividing t by 1982

• Adding t to 1982

• Subtracting t from 1982