Final Answer:
a) The linear model representing Mr. Hailey's weight after x months is ( y = -10x + 220).
b) After 6 months, Mr. Hailey would weigh ( 220 - (10 × 6) = 160 ) pounds.
c) After 14 months, Mr. Hailey would weigh ( 220 - (10 × 14) = 80 ) pounds. This weight is not considered healthy, as it is significantly below the normal weight range for an average adult. Rapid weight loss, such as losing 140 pounds in 14 months, can be associated with health risks and may indicate an unhealthy diet or other underlying health issues.
Step-by-step explanation:
The linear model representing Mr. Hailey's weight loss follows the form ( y = mx + b ), where ( y ) represents the weight, ( x ) denotes the number of months, ( m ) is the rate of weight loss per month, and ( b ) is the initial weight. In this scenario, Mr. Hailey loses 10 pounds per month, so the equation becomes ( y = -10x + 220 ), where 220 is his initial weight.
After 6 months, we calculate Mr. Hailey's weight by substituting ( x = 6 ) into the linear equation: ( y = 220 - (10 × 6) = 220 - 60 = 160 ) pounds. Hence, after 6 months on his diet, Mr. Hailey would weigh 160 pounds.
For 14 months, substituting ( x = 14 ) into the equation yields ( y = 220 - (10 × 14) = 220 - 140 = 80 \) pounds. However, this weight is notably low and may not be healthy. An 80-pound weight for an adult is typically considered significantly underweight and could indicate health concerns such as malnutrition or severe weight loss. It's important to consider a healthy weight range, lifestyle, and consult with a healthcare professional to ensure a safe and sustainable approach to weight loss.