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At the beginning of an experiment, there are 400 grams of contaminants. Each hour, three-fourths of the contaminants are filtered out.

A. Formulate a recursive sequence modeling the number of grams after "n" hours.

B. Use the model to calculate the amount of contaminants after the third hour of the experiment.

Respuesta :

MrRoyal

The recursive sequence is:[tex]T_n = \frac 14T_{n-1}[/tex] and there are 25 contaminants left after the third hour of the experiment

The recursive sequence

The initial number  of contaminant is 400.

If 3/4 contaminants are filtered out, there are 1/4 contaminants left.

So, the recursive sequence is:

[tex]T_n = \frac 14T_{n-1}[/tex]

Where T1 = 400

The number of contaminants after the third hour

This means that n = 3.

So, we have:

[tex]T_3 = \frac 14 * T_2[/tex]

[tex]T_2 = \frac 14 * T_1[/tex]

Substitute [tex]T_2 = \frac 14 * T_1[/tex] in [tex]T_3 = \frac 14 * T_2[/tex]

[tex]T_3 = \frac 14 * \frac 14 * T_1[/tex]

Substitute 400 for T1

[tex]T_3 = \frac 14 * \frac 14 * 400[/tex]

Evaluate

[tex]T_3 = 25[/tex]

Hence, there are 25 contaminants left after the third hour of the experiment

Read more about recursive sequence at:

https://brainly.com/question/1275192

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