Answer:
It will take 27 minutes.
Step-by-step explanation:
Let the exponential decay function is, [tex]y = a(b)^{x}[/tex], 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, [tex]\frac{a}{2} = a(b)^{6}[/tex]
⇒ [tex]b^{6} = 0.5[/tex]
⇒ b = 0.891 (Approximate)
Now, if y = 35 grams and a = 790 grams, then we can write
[tex]35 = 790(0.891)^{x}[/tex]
⇒ [tex]0.044 = (0.891)^{x}[/tex]
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)
