The radioactive substance cesium-137 has a half-life of 30 years. The amount At (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function. At = 523(1/2)^t/30 Find the initial amount in the sample and the amount remaining after 100 years. Round your answers to the nearest gram as necessary.
Initial amount: grams
Amount after 100 years: grams

Initial amount is 523 grams

Amount after 100 years is 52 grams

Step-by-step explanation:

General exponential function for radioactive substances is given by

A(t) = Ao(1/2)^t/t1/2

Where,

A(t) is the amount remaining after t years

Ao is the initial amount of the radioactive substance

t is the number of years required for the radioactive substance to decay to A

t1/2 is the half-life of the radioactive substance

Comparing A(t) = 523(1/2)^t/30 with the general exponential function

Initial amount (Ao) = 523 grams

A(t) = 523(1/2)^t/30

t = 100

A(100) = 523(1/2)^100/30 = 523×0.5^3.333 = 523×0.0992 = 51.8816 = 52 grams (to the nearest gram)

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

10 - 75

step-by-step explanation:

there's nothing attached so it's most likely anything in that range.