Question

The 1984 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atinosphere. The function f(x) = 10000.5)30 describes the amount, f(x), in kilograms, of a radioactive element remaining in the area x years after 1984 , if even 100 kibgrams of the radioactive element remains in the atmosphere, the area is considered unsafe for human habiation. Find r(00) and defermine it the area well be tate for human habitation by 2064 .

Answer 1

To find f(0), substitute x=0 into the function f(x). To determine if the area will be safe by 2064, substitute x=2064 into the function f(x) and check if the resulting value is less than 100 kilograms.

Step-by-step explanation:

The question asks us to find the value of f(0), and to determine if the area will be considered safe for human habitation by 2064.

To find f(0), we need to substitute x=0 into the given function. By doing so, we get:

f(0) = 10000.5^0*30 = 10000*30 = 300000

Therefore, the value of f(0) is 300,000 kilograms of the radioactive element.

To determine if the area will be considered safe for human habitation by 2064, we need to find the amount of the radioactive element remaining in the atmosphere in that year. To do so, we substitute x=2064 into the function:

f(2064) = 10000.5^2064*30

Calculating this value would require a calculator or computer program, as it involves a large exponent. If the resulting value is less than 100 kilograms, then the area will be considered unsafe for human habitation in 2064.