A substance has a half-life of 2.047 minutes. If the initial amount of the subst

Question

A substance has a half-life of 2.047 minutes. If the initial amount of the substance was 113.6 grams, how many half-lives will have passed before the substance decays to 7.1 grams? half-lives What is the total time of decay? min Carbon 14 as a half-life of 5, 730 years. A fossil is found that has 24% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year) yr The following equation represents the growth of bacteria in a particular food product, where t represents time in days and f(t) represents the number of bacteria. R(t) = 300e^The product cannot be eaten after the bacteria count reaches 1, 200,000. About how many days will it take before the product is inedible? (Round your answer to the nearest full day.) days

Explanation / Answer

half life = 2.047 minutes

initial amount = 113.6

setting up the equation

P = Po e^kt

1/2 = e^(2.047 k )

ln ( 1/2 ) = 2.047k

k = ln (1/2) / 2.047

k = -0.338616

decay constant = -0.338616

time it takes to decay to 7.1 grams

7.1 = 113.6e^( -0.338616 t )

7.1/ 113.6 = e^( -0.338616 t )

8.188 minutes

8.188 / 2.047 = 4

so it takes 4 half lives to decay to 7.1 grams

total time of decay = 8.19 minutes ( approx)

2) half life of carbon 14 = 5730 years

A = Ao e^ kt

1/2 = e^(5730 k )

k = ln (1/2) / 5730

k = -0.0001209

now plugging A= 0.24Ao

.24 = e^(-0.0001209 t )

t = 11804 years

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