Gold-192 is a radioactive isotope with a half-life of 4.95 hours. How long would it take for a 25 gram sample of Gold-192 to decay until only 2 grams remain? a. about 9.1 hours b. about 31 hours c. about 18 hours d. about 61.9 hours

Step-by-step explanation:

The formula you will need for this is:

where A is the amount after some decay has happened, A₀ is the intial amount, t is the time in hours, and H is the half-life in hours. Those values for us are:

A = 2 g

A₀ = 25 g

H = 4.95 hrs and

t = ?

Filling in:

Keep in mind that, because of the nature of the exponential form of this equation, you CANNOT simply multiply the 25 by the 1/2. Exponential equations don't work that way. Begin instead by dividing both sides by 25 to get

The goal is to get that t out from its exponential position. Do that by taking the natural log of both sides:

After you take the natural log of the right side, the property allows you to bring the exponent down out front:

Now divide both sides by ln(.5) to get

Simplify the left side out on your calculator to get

and then divide:

Finally, multiply both sides by 4.95 to get

3.643856(4.95) = t so

t = 18.0 hours which is choice C

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.