Question

The half-life of a radioactive substance is 1200 years. If the initial amount of the substance is 300 grams, give an exponential model for the amount remaining t years. What amount of substance remains after 1000 years?

Answer 1

N = 300/2^(1000/1200)

=170 (approx.)

Answer 2

Answer:

The amount of substance remains after 1000 years is 168.37 grams

Step-by-step explanation:

Given:

The half-life of a radioactive substance is 1200 years.

The initial amount of the substance is 300 grams

To find:

The amount of substance remains after 1000 years

Solution:

The exponential model for the amount A =A. $(0.5)^{\frac{t}{1200} }$

A is the initial amount

t is the time

The exponential model for the amount remaining t years can be given as  A = A. $(0.5)^{\frac{t}{1200} }$

The initial amount is given as 300 grams

Therefore A = 300

Sub A value in exponential model

A  = 300. $(0.5)^{\frac{t}{1200} }$

t = 1000 years

Substitute t value

A = 300$(0.5)^{\frac{1000}{1200} }$

A = 300$(0.5)^{\frac{5}{6} }$

A = 300(0.561)

A = 168.37 g

The exponential model for the amount remaining t years is 300. $(0.5)^{\frac{t}{1200} }$

Amount of substance remains after 1000 years is 168.37g

Final answer:

The amount of substance remains after 1000 years is 168.37 grams

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