In April 1986, a flawed reactor design played a part in the Chernobyl nuclear meltdown. Approximately 14252 becqurels (Bqs), units of radioactivity, were initially released into the environment. Only areas with less than 800 Bqs are considered safe for human habitation. The function \( f(x)=14252(0.5)^{\frac{x}{32}} \) describes the amount, \( f(x) \), in becqurels, of a radioactive element remaining in the area \( x \) years after 1986 . Find \( f(40) \), to one decimal place, in order to determine the amount of becqurels in 2026 .

To find the amount of radioactive element remaining in the area in 2026, we need to evaluate the function \( f(x) \) at \( x = 40 \) (since 2026 is 40 years after 1986). Let's calculate \( f(40) \): \[ f(40) = 14252 \left(0.5\right)^{\frac{40}{32}} \] First, calculate the exponent: \[ \frac{40}{32} = 1.25 \] Now calculate \( \left(0.5\right)^{1.25} \): \[ \left(0.5\right)^{1.25} \approx 0.3536 \] Now multiply: \[ f(40) = 14252 \times 0.3536 \approx 5033.59 \] Rounding to one decimal place, we get: \[ f(40) \approx 5033.6 \text{ Bqs} \] So, in 2026, the amount of becqurels in the area would be approximately 5033.6 Bqs.