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3 years ago

Find the slope from the pair of points

Mathematics

1 answer:

Rina8888 [55]3 years ago

5 0

What do we need to find the slope to? There is no picture

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An unknown radioactive element decays into non-radioactive substances. In 440 days the radioactivity of a sample decreases by 74

Neko [114]

Answer:

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.

3 0

3 years ago

Hi I'm a girl and if anyone need help come to me cause I'm here and I know every thing and I'm nice:)

alexira [117]

Uhmm ok thank uuuuuu

3 0

3 years ago

Read 2 more answers

CAN SOMEONE PLSSSSS ANSWER BOTH OF THESE QUESTIONS<br> I WILL MARK BRAINLIEST

Margaret [11]

Answer: B and C

Step-by-step explanation:

404 + 50 + 50 = 504

you are buying 144 magazines total

504/144 = cost of one magazine

cost of one = 3.50

you are paying $60 a year for 12 years

60 x 12 = 720

720/144 = 5

5 - 3.50 = 1.50

120x + 180x = 1080

300x = 1080

x = 1080/300

x = 3.6

3.6 x 60 = 216

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2 years ago

A town population of children increased from 367 to 421 during the past year which equation showes how to find the percentage in

klemol [59]

Answer:

5.7%

Step-by-step explanation:

421-367=24

24/421x100=5.7%

6 0

2 years ago

PLS HELP I WILL DO ANYTHING PLS

olganol [36]

447 with 0 remainder

4 0

2 years ago