World consumption of tin is running at the rate of thousand metric tons per year, where is measured in years and corresponds to 2014a. Find a formula for the total amount of tin that will be consumed within years of 2014b. When will the known world resources of 4900 thousand metric tons of tin be exhausted? [Tin is used mainly for coating steel (a "tin" can is actually a steel can with a thin protective coating of tin to prevent rust).

The chemical element tin (Sn), which is a member of Group 14 (IVa) of the periodic table and the family of carbon. The ancients were familiar with it as bronze, an alloy of copper and a soft, silvery-white metal with a bluish hue. Tin is frequently used in solder, metals for bearings, and the coating of steel food cans.

What is steel ?

Commercial iron is malleable when the right conditions are present, and it differs from cast iron by having a lower carbon content and any amount of carbon up to roughly 1.7 percent as an essential alloying ingredient.

let x(t) is the total consumption of tin at time t

dx/dt = 342 e

∫dx= ∫342e⁰⁰²dt

x(t) = 17100 e⁰⁰²t ⇒1

x(t) = 4900000

4900000= 17100 e⁰⁰²t

4900000/ 17100 = e⁰⁰²t

206.5497 = e⁰⁰²t

ln (206.5497) = e⁰⁰²t

=0.02t = 5.657g

t = 5.657g/ 0.02

= 202.89

=203

2014∝203= 2297

so resource of tin will be exhausted in 2297.

Therefore, the findings of the tin resource will be exhausted as 2297.

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