table of values help

Question

Celsium-137 has a half life of 30 years. For an initial amount of 96 grams, an equation that models the amount remaining after t years is: A(t)=144(1/2)^2/30

A. Complete the table below

Years Grams

0

30

60

90

120

150

B.Find the amount of Celsium-137 after 200 years

Answer 1

A)To complete the table, we simply need to evaluate the expression A(t) for the given values of t.

Using the formula A(t) = 144(1/2)^(t/30), we get:

Years Grams

0 144

30 72

60 36

90 18

120 9

150 4.5

B)The equation given to model the amount remaining after t years is:

A(t) = 96*(1/2)^(t/30)

To find the amount of Celsium-137 after 200 years, we can substitute t = 200 into the equation:

A(200) = 96*(1/2)^(200/30)

Simplifying:

A(200) = 96*(1/2)^(20/3)

A(200) = 96*(1/2)^(6.6667)

A(200) ≈ 1.647 grams (rounded to 3 decimal places)



Therefore, the amount of Celsium-137 remaining after 200 years is approximately 1.647 grams.