Answer to Question #128267 in Algebra for ysabe castro

Question

a) From the early 1970’s through 2001, the rate of obesity in young American children, ages 6 to 11, has shown a linear increase. In 1988, approximately 10.23 % of 6-11 year old American children were obese. By 2001, the rate of obese American had risen to 15 %. Write a linear model that would model these data where t = time in year after 1988 and R is the Rate of obesity as a percentage. Round your answer to two decimal places if necessary.
Solution:
b) Use this model to predict the 2016 obesity rate among 6-11 year old American chil

Answer 1

(a). The slope-intercept form of the equation look like: y=mx+b

 where m=slope (the rate of increase ) and (0,b) is the y intercept

The linear model the researcher wants looks like:  R = mt + b

where m=increase in rate of obesity

(0,b) is the initial value of R

t =time in years after 1988

The researcher knows that:

 In 1988 (t=0), the rate (R) was 10.23%, so we have the point (0,10.23) this is (t₁,R₁)

 In 2001 (t=13), the rate was 15%, so we have the point (13,15); and (t₂,R₂)

With two data points, we find the equation of the line using the point-slope form of an equation:

(y-y₁) = m (x-x₁)

(y-y₁) = {(y₁-y₂)/(x₁-x₂)}(x-x₁)

now y=R ,y₁=R₁ ,y₂=R₂ and x=t , x₁=t₁ , x₂=t₂

(R-R₁) = {(R₁-R₂)/(t₁-t₂)}(t-t₁)

(R-10.23) = {(15-10.23)/(13-0)}(t-0)

(R-10.23) = {(4.77)/13}(t)

(R-10.23) = 0.36 t

R-10.23 = 0.36t

R = 0.36t +10.23

(b). R = 0.36 t +10.23

this linear model is for 1988 so t₁=0

for 2016 , t₂ = 28 { t₂ = 2016 - 1988 = 28 }

R = 0.36 (t₂-t₁) +10.23

R = 0.36 (28-0) + 10.23

R = 0.36 (28) + 10.23

R = 10. 08 + 10.23

R = 20.31

2016 obesity rate among 6-11 year old American children is 20.31%.