Question

During a science experiment, Cesar sets up a group of filter that removes contaminants from a liquid sample. Each filter removes 94.8% of the remaining contaminants. Which recursive formula describes the fraction of contaminants still remaining in the liquid sample after passing through n filters?

Answer 1

Using an exponential function, the recursive formula that describes the fraction of contaminants still remaining in the liquid sample after passing through n filters is given by:

$A[n] = (0.052)^n$

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem, considering an initial fraction of A(0) = 100% = 1, the decay rate is of r = 0.948, hence the formula is:

$A[n} = (1 - r)^n$

$A[n] = (0.052)^n$

More can be learned about exponential functions at brainly.com/question/25537936