Final answer:
To model the distribution each year of cans made from recycled aluminum, use the exponential function equation P(t) = 420,000 * (1.9)^t, where P(t) represents the number of cans distributed in year t.
Step-by-step explanation:
To write an exponential function equation to model the distribution each year of cans made from recycled aluminum, we need to determine the initial amount of cans distributed in 2010 and the growth rate. In 2010, the manufacturer distributed 420,000 cans made from the recycled cans it had previously distributed. Therefore, the initial amount of cans distributed in 2010 is 420,000. The recycling rate indicates that each year, a certain percentage of the cans previously distributed will be recycled and distributed again. Let's assume that the recycling rate is 90%, meaning that 90% of the previously distributed cans are recycled and distributed again each year. The growth factor of an exponential function is equal to 1 plus the percentage growth rate. Therefore, the growth factor is 1 + 0.9 = 1.9 (1 + 90%).
The exponential function equation to model the distribution each year of cans made from recycled aluminum can be written as:
P(t) = 420,000 * (1.9)^t
Where P(t) represents the number of cans distributed in year t.