Question

Element X decays radioactively with a half life of 6 minutes. If there are 790 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 35 grams?

Answer 1

Answer:

It will take 27 minutes.

Step-by-step explanation:

Let the exponential decay function is, $y = a(b)^{x}$, where a is the initial value and b is the rate of decay.

Now, 6 minutes is the half-life of the radioactive element.

So, $\frac{a}{2} = a(b)^{6}$

⇒ $b^{6} = 0.5$

⇒ b = 0.891 (Approximate)

Now, if y = 35 grams and a = 790 grams, then we can write

$35 = 790(0.891)^{x}$

⇒ $0.044 = (0.891)^{x}$

Now, taking log in both sides, we get

log (0.044) = x log (0.891)

⇒ x = 27 minutes.

Therefore, it will take 27 minutes. (Answer)