The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?

Where represent the half life and the intial amount would be

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

If we apply natural log on both sides we got:

And solving for t we got:

So then would takes about 14.26 hours in order to have  95% of the lead to decay

Step-by-step explanation:

For this case we can define the variable of interest amount of Pb209 and for the half life would be given:

Where represent the half life and the intial amount would be

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

If we apply natural log on both sides we got:

And solving for t we got:

So then would takes about 14.26 hours in order to have  95% of the lead to decay

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500