Ask question

Ask question

All categories

3 years ago

5

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for

carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.

1 answer:

Rudik [331]3 years ago

8 0

A(t) = Ao*e^(-rt)

-rt = ln [ A(t)/ Ao]

t = - ln [ A(t)/ Ao] / r

r= 0.0124% = 0.0124/100 = 0.000124

A(t)/A0 = 10% = 10/100 = 0.1

Now substitute

t = - ln [0.1] / 0.000124 = 2.3025851 / 0.000124 = 18,569 years

Your result will depend on how you round ln(0.1).

You might be interested in

Probabilities with possible states of nature: s1, s2, and s3. Suppose that you are given a decision situation with three possibl

amm1812

Answer:

1. $P(s_1|I)=\frac{1}{11}$

2. $P(s_2|I)=\frac{8}{11}$

3. $P(s_3|I)=\frac{2}{11}$

Step-by-step explanation:

Given information:

$P(s_1)=0.1, P(s_2)=0.6, P(s_3)=0.3$

$P(I|s_1)=0.15,P(I|s_2)=0.2,P(I|s_3)=0.1$

(1)

We need to find the value of P(s₁|I).

$P(s_1|I)=\frac{P(I|s_1)P(s_1)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_1|I)=\frac{(0.15)(0.1)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_1|I)=\frac{0.015}{0.015+0.12+0.03}$

$P(s_1|I)=\frac{0.015}{0.165}$

$P(s_1|I)=\frac{1}{11}$

Therefore the value of P(s₁|I) is $\frac{1}{11}$ .

(2)

We need to find the value of P(s₂|I).

$P(s_2|I)=\frac{P(I|s_2)P(s_2)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_2|I)=\frac{(0.2)(0.6)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_2|I)=\frac{0.12}{0.015+0.12+0.03}$

$P(s_2|I)=\frac{0.12}{0.165}$

$P(s_2|I)=\frac{8}{11}$

Therefore the value of P(s₂|I) is $\frac{8}{11}$ .

(3)

We need to find the value of P(s₃|I).

$P(s_3|I)=\frac{P(I|s_3)P(s_3)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_3|I)=\frac{(0.1)(0.3)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_3|I)=\frac{0.03}{0.015+0.12+0.03}$

$P(s_3|I)=\frac{0.03}{0.165}$

$P(s_3|I)=\frac{2}{11}$

Therefore the value of P(s₃|I) is $\frac{2}{11}$ .

4 0

2 years ago

Steve drove at a constant rate to the beach for a vacation. In the equation below, t is the time in hours it took Steve to drive

hjlf

Could you please provide the equation and the rest of the question?

7 0

2 years ago

PHOTO ADDED PLEASE HELP

asambeis [7]

Exact form: 10/9 decimal form: 1.111 mixed number form: 1 1/9

3 0

2 years ago

Read 2 more answers

The recycling club has a goal to recycle 2,000 pounds of newspaper this year. They have already recycled 1,585 pounds. How many

Burka [1]

Hi lola66795 i know the answer the answer is 415 pounds what you have to do is subtract 1585 from 2000 and you will get 415

3 0

3 years ago

PLEASE HELP!! ILL GIVE YOU BRAINLIEST!!

schepotkina [342]

Answer:

because when x ing a positive to a negative it will give you a negative however if you x a negative and a negitive it will give a positive

Step-by-step explanation:

7 0

2 years ago