monet83

monet83

12.03.2020 •

Mathematics

What is the equation of the line of reflection in the following coordinate plane?

https://dw6y82u65ww8h.cloudfront.net/organisations/328/1c2c4146-6f78-4bce-b26d-ec142f95b787/img_test_coordinate_plane_reflection.gif

y = 1
x = 1
x = 0
y = 2

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Ответ:

janiya666

07.11.2021

a) The half life of the element is 231 days.

b) It is going to take around 31.5 days for a sample of 100 mg to decay to 91 mg.

Step-by-step explanation:

The radioactivity of the sample can be modeled by the following exponential equation:

$R(t) = R(0)e^{-rt}$

In which t is the time in days, r is the decay rate and R(0) is the initial radioactive percentage.

We have that:

In 440 days the radioactivity of a sample decreases by 74 percent.

This means that R(440) = 0.26R(0) .

This helps us find r.

$R(t) = R(0)e^{-rt}$

$0.26R(0) = R(0)e^{-440r}$

$e^{-440r} = 0.26$

Applying ln to both sides.

$\ln{e^{-440r}} = \ln{0.26}$

-440r = -1.347

r = 0.003

(a) What is the half-life of the element?

This is t when R(t) = 0.50R(0)

$R(t) = R(0)e^{-rt}$

$0.50R(0) = R(0)e^{-0.003t}$

$e^{-0.003t} = 0.5$

Again, we apply ln to both sides of the equality.

$\ln{e^{-0.003t}} = \ln{0.5}$

-0.003t = -0.693

t = 231

The half life of the element is 231 days.

(b) How long will it take for a sample of 100 mg to decay to 91 mg?

This is t when R(t) = 0.91R(0)

$R(t) = R(0)e^{-rt}$

$0.91R(0) = R(0)e^{-0.003t}$

$e^{-0.003t} = 0.91$

$\ln{e^{-0.003t}} = \ln{0.91}$

-0.003t = -0.09

t = 31.44

It is going to take around 31.5 days for a sample of 100 mg to decay to 91 mg.

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