Predlcm amend 32% oprer consumed in the United Sutes (51.3milion kms) was recycl

Question

Predlcm amend 32% oprer consumed in the United Sutes (51.3milion kms) was recycled. d Papr Association sates that, hased on previous data, its goal is to % of piper have 48% movery by 2025. a) Assuming linear growth, find the equation of a line that can be used to describe these data. b) Predict the recovery rate in the year of 2027 ) Dw your equation above represent a function? Ifsot, then write "not a function" and explain why. If yes, explain why and then find its domain and its range. Answerk

Explanation / Answer

a) Assuming linear growth:-

equation of a linear graph :- y=mx+c, where y represents dependable variable, m is the slope, x is the independent variable and c is constant. As it is linear growth so c will be zero hence y=mx. now here y is the recovery rate and x represents the respective year.

Now to find m i.e slope the equation is m= (y2-y1)/(x2-x1). Here y2 is 48%, y1 is 32%, x2 is 2025 and x1 is 2005.

hence m= (48-32)/(2025-2005)= 0.16/20 = 0.008.

Hence the equation is y=0.008x.

b) the recovery rate in 2027 will be as follows:-

Here x=2 as the difference between 2025-2027

y=0.008x2 = 0.016

recovery rate in 2027 will be 0.016+0.48 = 0.496= 49.6% (we have added 48 because 48 is the present recovery rate of 2025 and we need to find for 2027. The recovery difference is 0.016).

c) The above equation represents function as follows:-

y = 0.008x where x is (x2-x1).

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