N(t)=650,000(0.515)

Question

Although the people in a country throw 1500 aluminum cans in the trash every second of every day, 51.5% of the aluminum in the cans is recycled. If a beverage company distributes 650,000 cans, the amount of aluminum still in use after t years can be made into N cans where N(t)=650,000(0.515)^t. How many cans can be made from the original 650,000 cans after 4 years?

Answer 1

The function N(t)=650,000(0.515)^t calculates the number of

the original 650,000 are still in use after "t" years.  The function

needs to be evaluated when t=4.  So, rewrite the function as...

 

     N(4)=650,000(0.515)⁴.........substitute 4 for "t"

            =650,000(0.0703)........evaluate exponent

∴ N(4)=45,723.80...................simplify

 

Approximately 45,724 recycled cans are still in use after 4 years.