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Answer:
Approximately 3 grams left.
Step-by-step explanation:
We will utilize the standard form of an exponential function, given by:
[tex]f(t)=a(r)^t[/tex]
In the case of half-life, our rate r will be 1/2. This is because 1/2 or 50% will be left after t half-lives.
Our initial amount a is 185 grams.
So, by substitution, we have:
[tex]\displaystyle f(t)=185\big(\frac{1}{2}\big)^t[/tex]
Where f(t) denotes the amount of grams left after t half-lives.
We want to find the amount left after 6 half-lives. Therefore, t = 6. Then using our function, we acquire:
[tex]\displaystyle f(6)=185\big(\frac{1}{2}\big)^6[/tex]
Evaluate:
[tex]\displaystyle f(6)=185\big(\frac{1}{64}\big)\approx2.89\approx 3[/tex]
So, after six half-lives, there will be approximately 3 grams left.