Question

A truck radiator holds 5 gal and is filled with water. A gallon of water is removed from the radiator and replaced with a gallon of antifreeze; then a gallon of the mixture is removed from the radiator and again replaced by a gallon of antifreeze. This process is repeated indefinitely. How much water remains in the tank after this process is repeated 3 times? 5 times? n times?

Answer 1

5 * .8^3

5 * .8^5

5 * .8^n

Answer 2

term -- water -- antifreeze
1 ........ 5 ....... 0
2 ......... (.8)5 ....... 1 ----- water is 5(.8)
3 start with 5(.8) remove .2 of that leaving 5(.8)^2 = 3.2 gallons of water
4 starts with 5(.8)^2 , remove .2 of that leaving 5(.8)^3
5 ..................... leaving 5(.8)^4
...
n ..................... leaving 5(.8)^(n-1)

Answer 3

go with R_scott's answer

I counted the initial stage as the first process