Question

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.

Answer 1

Yes, I know. This is very late, however if any more of you need help on this topic, here you go!

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| Algebra 2 A |

U7 L3: (QUIZ P1)

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Graph the exponential function.

1.
`y=3^x`

• Third Graph (a.k.a. Option C)

Graph the exponential function.

2.
`y=2(4.5)^x`

• First Graph (a.k.a. Option A)

Graph the function.

3.
`y=4((1)/(5) )^x`

• Fourth Graph (a.k.a. Option D)

Graph the function.

4.
`y=3(2)^x^+^1-4`

• Second Graph (a.k.a. Option B)

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.

• D)
  `y=790((1)/(2) )^(1)/(78)^x; 0.429kg`

6. Using a graphing calculator to evaluate
`e^1^.^6` to four decimal places.

• A) 4.9530

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?

• C) about 5.01 times as much energy

8. Graph the logarithmic equation.

`y=log_(5) x`

• Third Graph (a.k.a. Option C)

9. Graph the function.

`y=log(x+1)+1`

• First Graph (a.k.a. Option A)

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Hope this helps! Good luck!

Answer 2

Write an exponential function that models the decay of this material.

The function is described by the half-life equation which is expressed as:

An = Ao e^-kt where An is the amount left after t time, Ao is the initial amount and k is a constant.

Find how much radioactive material remains after 18 hours. Round your answer to the nearest thousandth.

1/2Ao = Ao e^-k(78)
k = 8.89 x 10^-3

An = 790e^-8.89 x 10^-3(18)
An = 673.22 kg