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# Exponential Decay (Half-Life) $A_t=A_0(\frac{1}{2})^\frac{t}{h}$

1. 1
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance has a half-life of 3 hours. If you start with 100 g, what mass will remain after 12 hours?

(Note: This lesson includes a brief explanation of half-life.)
2. 2
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance has a half-life of 18 hours. If you start with 18 g, what mass will remain after 3 days?
3. 3
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance has a half-life of 15 hours. If you start with 100 kg, what mass will remain after 2 days?
4. 4
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance has a half-life of 20 hours. How long will it take for 400g to decay to 50g?
5. 5
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance has a half-life of 7 hours. How long will it take for 768g to decay to 24g?
6. 6
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance has a half-life of 5 days. How long will it take for 1312 kg to decay to 82 kg?
7. 7
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  If you have 68g of a radioactive substance that decays to 17g after 12 days, what is the half-life?
8. 8
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  If you have 192g of a radioactive substance that decays to 3g after 18 years, what is the half-life?
9. 9
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance decays to $\frac{1}{16}$ of its original amount after 24 days. What is the half-life?  Good test question!
10. 10
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  A radioactive substance decays to $\frac{1}{32}$ of its original amount after 15 days. What is the half-life? 
11. 11
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  How long will it take for a radioactive substance to decay to $\frac{1}{4}$ of its original amount, if the half-life is 40 minutes?
12. 12
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  How long will it take for a radioactive substance to decay to 25% of its original amount, if the half-life is 5 days?  Good test question!
13. 13
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  How long will it take for a radioactive substance to decay to 12.5% of its original amount, if the half-life is 9 days?
14. 14
Use the equation $A_t=A_0(\frac{1}{2})^\frac{t}{h}$ to solve.  What is the half-life of a radioactive substance if it decays to 6.25% of its original amount after 32 minutes?

$$e=mc^2$$