Exponential Growth/Decay PLEASE HELP/Problem in the description.

Question

In many cases, removing dangerous chemicals from waste sites can be modeled using exponential decay. This is a key reason why such cleanups can be dramatically expensive. Suppose for a certain site there are initially 20 parts per million of a dangerous contaminant and that our cleaning process removes 5% of the remaining contaminant each day.

How much contaminant (in parts per million) is removed during the first five days? Round your answer to two decimal places.

 

_____________ ppm

Answer 1

Use the formula

 

P = P_o(1 - r)^t

 

where:

P = amount of contaminants (ppm)

P₀ = initial amount

t = time (in days)

r = rate (in decimal)

 

So you have

 

P = 20(1 - 0.05)^t

 

P = 20(0.95)^t

 

 

Now just evaluate P when t=5.

Answer 2

If we remove 5% per day... Then at the end of each

day we have 95% left of what we started with ....

 

A_n = A₀(1-r)ⁿ

A_n = final amount left

A₀ = initial amount = 20ppm

r = decay rate as decimal = .05

n = #decay cycles ...  = 5

 

A_n = 20(1-.05)⁵

A_n = 20(.95)⁵

 

Amount removed will be

20 - A_n ppm