The following table relates the weight of garbage in tons to the time in years s

Question

The following table relates the weight of garbage in tons to the time in years since 1984. Environmentalists decided that this relationship is exponential. Use the table to answer the following questions.

Number of years since 1984

1

3

5

7

9

Weight of garbage (in tons)

2580

3715.2

5349.888

7703.83872

11093.52776

a. What is the 1-year growth factor?

b. What was the weight of the garbage in 1984?

c. Define the rule for the function function, d, that gives the number of years since 1984 in terms of the weight of the garbage, x (in tons).
d(x)=

Number of years since 1984

1

3

5

7

9

Weight of garbage (in tons)

2580

3715.2

5349.888

7703.83872

11093.52776

Explanation / Answer

a)1-year growth factor =3715.2/2580

1-year growth factor=1.44

b)in 1984, d =0

weight of the garbage in 1984 =2580/1.44

weight of the garbage in 1984 =1791.66667 tons

c)x=(1791.66667)*(1.44)d

(1.44)d=(x/1791.66667)

(1.44)d=(0.000558x)

d=ln1.44(0.000558x)

function function, d, that gives the number of years since 1984 in terms of the weight of the garbage, x (in tons).
d(x)= ln1.44(0.000558x)

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