5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after. 18 hours. Round your answer to the nearest thousandth.
My answer: y = 790(1/2)^1/78x; 673.233 kg
7. The table shows the location and magnitude of some notable earthquakes. How many times more energy was released by the earthquake in Mexico than by the earthquake in Afghanistan?
The Richter Scale measure for Afghanistan is 6.9 and the Richter Scale measure for Mexico is 7.6
A. about 42.36 times as much energy
B. about 0.70 times as much energy
C. about 5.01 times as much energy**
D. about 21 times as much energy
These are questions from the Logarithmic Functions as Inverses Lesson 3 Unit 7 so if anyone knows the answers, that'd be helpful.
Just took the quiz.
C
A
D
B
D
A
C
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A
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When when life gives you lemons is correct! He saved not only my Math grade, but my job and marriage. Thank you!
My other answer now that i look at it again would be 0.70. I just subtracted the two
For the first question:
To model the decay of the radioactive material, we can use the exponential decay formula:
y = A(1/2)^(x/k),
where:
- y represents the amount of radioactive material remaining after x hours
- A represents the initial amount of the material, in this case 790 kg
- (1/2) represents the decay factor since the half-life is 78 hours
- x represents the number of hours passed since the initial amount
- k represents the half-life, in this case 78 hours
Therefore, the exponential function that models the decay of this material is:
y = 790(1/2)^(x/78)
To find the amount of radioactive material remaining after 18 hours, we can substitute x = 18 into the equation:
y = 790(1/2)^(18/78)
Calculating this equation will give the result, which when rounded to the nearest thousandth, is 673.233 kg.
So, your answer of 673.233 kg is correct.
For the second question:
To compare the energies released by the earthquakes in Mexico and Afghanistan, we need to consider that each increase in 1 on the Richter scale corresponds to a tenfold increase in energy released.
The difference in Richter scale measures between Mexico (7.6) and Afghanistan (6.9) is:
7.6 - 6.9 = 0.7
Therefore, the earthquake in Mexico released 10^0.7 times more energy than the one in Afghanistan.
Using a calculator, we find that 10^0.7 ≈ 5.011.
So, the earthquake in Mexico released about 5.01 times as much energy as the earthquake in Afghanistan.
Therefore, the correct answer is option C: about 5.01 times as much energy.