The following table relates the weight of garbage in tons to

The following table relates the weight of garbage in tons to the tune in years since 1984. It is known that the relationship is exponential. Use the table to answer the following questions. a. What is the 2-year growth factor? b. What the 1-year percent change? % c. What was the weight of the garbage in 1982? tons

Solution

a) Weight of grabage( x=3)/Weight of garbage( x =1) = 3715.2/2580 = 1.44

2 - year growth factor = 1.44

b) Let garbage function be denoted as:

b) G(n) = Go(b)^x

2580 = Go(b)^1

3715..2 = Go(b)^3

So, b^2 = 3715.2/2580 = 1.44

b = 1.2

G(n) = Go(1.2)^x

for x = 1 G(1) = Go(1.2)

So, 1 year % change = [(Go(1.2) - Go)/Go]*100 = 20%

c) 1982 means x= -2

G(n) = Go(1.2)^x

2580 = Go(1.2)   where Go = garbage in 1984

So, Go = 2150 tons

So, G(n) = 2150(1.2)^x    ( model for garbage)

Now for 1982 ; x=-2

we get G(-2) = 2150(1.2)^-2

= 1493.06 tons