Answer:
About 5, 805 grams remaining.
Step-by-step explanation:
We are given that every 27 years, the mass of Element X decreases by half.
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]\displaystyle f(t)=a(r)^t[/tex]
Where a is the initial amount, r is the rate, and t is the time, in this case years.
Since it is halved, our rate r is 1/2.
Since it is halved for every 27 years, for t, it will be t/27.
Therefore, our function is:
[tex]\displaystyle f(t)=a\Big(\frac{1}{2}\Big)^{t/27}[/tex]
Our initial sample is 7,900 grams. Hence, a = 7900:
[tex]\displaystyle f(t)=7900\Big(\frac{1}{2}\Big)^{t/27}[/tex]
We want to find the remaining amount after 12 years. So, t = 12. Use a calculator:
[tex]\displaystyle f(12)=7900\Big(\frac{1}{2}\Big)^{12/27}\approx5805\text{ grams}[/tex]
After 12 years, there will be about 5805 grams remaining.
Answer:
About 5, 805 grams remaining.
Step-by-step explanation:
We are given that every 27 years, the mass of Element X decreases by half.
We can write an exponential function to model the situation. The standard exponential function is given by:
→ f(t)=a(r)^t
Where a is the initial amount, r is the rate, and t is the time, in this case years.
Since it is halved, our rate r is 1/2.
Since it is halved for every 27 years, for t, it will be t/27.
Therefore, our function is:
→ f(t)=a(1/2)^t/27
Our initial sample is 7,900 grams. Hence, a = 7900:
→ f(t)=7900(1/2)^t/27
We want to find the remaining amount after 12 years. So, t = 12. Use a calculator:
→ f(12)=7900(1/2)^12/27 ≈5805 grams
After 12 years, there will be about 5805 grams remaining.
