a radioactive substance has an initial mass of 100 grams and its mass halves every 4 years. Which expression shows the number of grams remaining after t years?1) 100(4)^t/42) 100(4)^-2t3)100(1/2)^t/44)100(1/2)^4t
Accepted Solution
A:
We start with a mass of[tex]100 = 100 \cdot \left(\dfrac{1}{2}\right)^0[/tex]After 4 years, we have[tex]50= 100 \cdot \left(\dfrac{1}{2}\right)^1[/tex]After 8 years, we have[tex]25= 100 \cdot \left(\dfrac{1}{2}\right)^2[/tex]So, as you can see, the general formula is[tex]m = 100 \cdot \left(\dfrac{1}{2}\right)^{\frac{t}{4}}[/tex]