4. Provide Solutions to the following modeling problems A superhero is rendered

Question

4. Provide Solutions to the following modeling problems A superhero is rendered powerless when exposed to 65 or more grams of a certain element. A 700 year old rock that originally contained 750 grams of this element was recently stolen from a rock museum by the superhero's nemesis. The half-life of the element is known to be 200 years. a) I. II. How many grams of the element are still contained in the stolen rock? For how many years can this rock be used by the superhero's nemesis to render the superhero powerless?

Explanation / Answer

i. N(t) = N0 e-t

Given N0 = 750 t1/2 = 200 t = 700

= ln 2 / t1/2 = ln 2 / 200

= 0.0035

N = 750 * e-0.0035*700

=> N = 66.29 gm

ii. N = 65 N0 = 66.29

65 = 66.29 * e-0.0035t

=> -0.0035t = ln (65/66.29)

=> -0.0035t = -0.02

=> t = 5.714 years.

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