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The 1985 1985 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atmosphere. The function f left parenthesis x right parenthesis equals 1000 left parenthesis 0.5 right parenthesis Superscript StartFraction x Over 30 EndFraction f(x)=1000(0.5) x 30 describes the​ amount, f(x), in​ kilograms, of a radioactive element remaining in the area x years after 1985 1985. If even 100 kilograms of the radioactive element remains in the​ atmosphere, the area is considered unsafe for human habitation. Find ​f( 40 40​) and determine if the area will be safe for human habitation by 2025 2025.

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Luv2Teach

Answer:

Step-by-step explanation:

If I'm understanding this correctly, the rate of decay function is

[tex]f(x)=1000(.5)^{\frac{x}{30}}[/tex]

and we want to solve for the amount of element left after x = 40 years.  That would make our equation

[tex]f(40)=1000(.5)^{1.33333333333}[/tex]

Multiply the repeating decimal by .5 to get

f(40) = 1000(.3968502631)

and f(40) = 396.85

So no, it's not safe for human habitation.