Factorize 5r⁸t⁵

he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost

elena-s [515]

Answer:

The bones were 12,485 years old at the time they were discovered.

Step-by-step explanation:

Amount of the element:

The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

$A(t) = A(0)e^{-kt}$

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The radioactive element carbon-14 has a half-life of 5750 years.

This means that $A(5750) = 0.5A(0)$ , and we use this to find k. So

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-5750k}$

$e^{-5750k} = 0.5$

$\ln{e^{-5750k}} = \ln{0.5}$

$-5750k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{5750}$

$k = 0.00012054733$

So

$A(t) = A(0)e^{-0.00012054733t}$

A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?

Had 100 - 77.8 = 22.2% remaining, so this is t for which:

$A(t) = 0.222A(0)$

Then

$0.222A(0) = A(0)e^{-0.00012054733t}$

$e^{-0.00012054733t} = 0.222$

$\ln{e^{-0.00012054733t}} = \ln{0.222}$

$-0.00012054733t = \ln{0.222}$

$t = -\frac{\ln{0.222}}{0.00012054733}$

$t = 12485$

The bones were 12,485 years old at the time they were discovered.

8 0

3 years ago

Chanel is going to paint a chervron design on her wall using the template. She will need to paint 50 of the templates. How many

sashaice [31]

Answer:

350 in²

Step-by-step explanation:

Assuming the solid likes are the design. So we see two parallelograms there.

Area of 1 parallelogram = base x height. Since we have a joint height, we will multiply the total height with the base (both have the same base length) to get the area of 1 design.

1 design = 3.5 x 2 = 7 in²

50 designs = 7 x 50 = 350 in²

8 0

3 years ago

Can you guys help me please!!

ella [17]

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1.C

2.C

3.D

4.D

5.D

6.A

7.C

8.B

9.A

10.C

11.A

12.B

13.D

14.C

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7 0

3 years ago

27x 5 + 9x 4 - 18x 3) 9x 2

notka56 [123]

In guessing it's 2,106.......

4 0

3 years ago

What is 3 4/5 times 2 1/3 ?<br> Your answer

Mazyrski [523]

The answer to this question is 8.86666666667

3 0

3 years ago

Factorize 5r⁸t⁵ - 3r⁴t⁴​

Factorize 5r⁸t⁵ - 3r⁴t⁴