Help please The 1985 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atmosphere. The function \( f(x) = 1000(0.5)^{\frac{x}{30}} \) describes the amount, \( f(x) \), in kilograms, of a radioactive element remaining in the area \( x \) years after 1985. If even 100 kilograms of the radioactive element remains in the atmosphere, the area is considered unsafe for human habitation. Find \( f(40) \) and determine if the area will be safe for human habitation by 2025.\( f(40) = \) (Type an integer or a decimal rounded to the nearest tenth as needed.)Will the area be safe for human habitation by 2025?- A. Yes, because by 2025, the radioactive element remaining in the area is greater than 100 kilograms.- B. No, because by 2025, the radioactive element remaining in the area is greater than 100 kilograms.- C. Yes, because by 2025, the radioactive element remaining in the area is less than 100 kilograms.- D. No, because by 2025, the radioactive element remaining in the area is less than 100 kilograms.

Given: fx=10000.5x30Substitute 40 for x in the above expression. f40=10000.54030=396.85 The radioactive element in the atmosphere in the year 2025 is 396.85 kg. As per the given conditions if even 100 kg of radioactive element remain in the atmosphere then the area is considered to be unsafe. Now, in the year 2025, the amount of radioactive element in the atmosphere is 396.86 kg that is very much greater than 100 kg. Hence, the area is not safe. Therefore, option (b) No, because by 2025 the radioactive element in the area is greater than 100 kg is the correct option.