Question

Half of the substance to remain is called the half-life of the substance.

The half-life of a pesticide is 10 years. A farmer initially applies 200 grams of the
pesticide to a fence post.
Complete the following statements.
After 20 years, there are
grams of pesticide left. Round your answer
to the nearest whole gram.
After 60 years, there are
grams of pesticide left. Round your answer
to the nearest hundredth of a gram.
After
years, there are approximately 1.03 grams of pesticide
left. Round your answer to the nearest whole year.

Answer 1

Instructions are below.

Explanation:

To calculate the final amount of a given substance, we need to use the following formula:

final amount= initial amount / (2^n)

n= elapsed time / half-life

For 20 years:

n= 20/10= 2

Final amount= 200/(2^2)

Final amount= 50 grams

For 60 years:

n= 60/10= 6

Final amount= 200/ (2^6)

Final amount= 3.125 grams

To calculate the elapsed time it is more complicated:

elapsed time= ln(ending amount/beginning amount) / (-decay constant)

ln= natural logarithm

decay constant= ln(2) / half-life

decay constant= 0.0693

elapsed time= ln(1.03/200) / (-0.0693)

elapsed time= 76.028

Prove:

n= 76.02/10= 7.602

Final amount= 200/(2^7.602)= 1.03 grams