Question

Oxford currently generates 77,400 tons of garbage per year, but the city is launching somerecycling initiatives to bring that number down. If, as a result, the amount of garbagedecreases by 14% each year, then how much garbage will be generated annually 17 yearsfrom now?If necessary, round your answer to the nearest tenth,

Answer 1

$5959.6$

1) Since we were told that Oxford is in its battle to reduce the garbage by 14% per year. Then we can write an exponential model to calculate the quantity of garbage 17 yrs from now, assuming this pace will remain constant.

The model:

$y=77400(0.86)^x$

2) Plugging into that the given data:

$\begin{gathered} y=77400(1-0.14)^{17} \\ y=77400(0.86)^{17} \\ y=5959.56\approx5959.6 \end{gathered}$

Thus, the answer is 5959.6 tons 17 yrs from now