The 1987 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 describes the amount, f(x), in kilograms, of a radioactive element remaining in the area x years after 1987. if even 100 kilograms of the radioactive element remains in the atmosphere, the area is considered unsafe for human habitation. find f(80) and determine if the area will be safe for human habitation by 2067.
The equation tells you the half-life is 30 years. In 90 years, 3 half-lives will have passed, so the decay will be to (1/2)^3 = 1/8 its original level. Radiation will not have decayed to 1/10 its original level in 80 years. The area will be unsafe in 2067.
