Related Rates: Choose only ONE option: aneurysm or BMI A research team in the UK
ID: 2831754 • Letter: R
Question
Related Rates: Choose only ONE option: aneurysm or BMI A research team in the UK (Journal of Health Services Research & Policy Vo) 13 No 3, 2008: 158-166) calculated overall prescription drug costs to patients relative to body mass. The team used Body Mass Index as a base for investigating whether weight management could save money over the long term. The team found that there was a predictable increase in drug costs with increasing BMI, to which Mr. Jackinsky has curve-fit a trend line with the equations below. The increase in costs was due to more types of medications prescribed to heavier patients, as well as higher doses prescribed to heavier patients. epislon/yr = 0.1219(BM/men)2.0122 /yr= 0.9761 (BM/women,)1.3877 1 = $1.49USD Part 1: i: Find the estimated annual prescription cost in USD associated with your gender with a BMI of 22kg/m2; ii: Find the estimated annual prescription savings in USD when compared to an individual of your gender with a BMI of 35kg/m2. Part 2: i: Find the rate at which the prescription price (in USD) is increasing associated with a BMI of 22kg/m2. ii: What is the rate of change of the annual prescription costs associated with a BMI of 35kg/m2? Part 3: Calculate how much money would be saved on prescriptions annually if 2.5 million individuals of your gender were able to decrease their BMI from 35kg/m2 to 22kg/m2; would you recommend weight loss to your patients to help reduce their healtheare costs?Explanation / Answer
1(i) BMI=22 Kg/m^3 then estimated anual perciption cost for women=106.06 $
since 1 euro=1.49 usd
1(ii)BMI=35 Kg/m^3 then estimated anual perciption cost=202.01 $
Hence saving=95.95 $
2(i)rate=106.06/(95.95)=1.105
2(ii)rate=202.01/95.95=2.10
3)money saved if 2.5 million individuals were able to decrease BMI from 35 to 22 Kg/m^3 =2.5*95.95=239.87 million $