*the half life of radium is 1690 years. if 70 grams are present now, how much will be present in 450 years?*

**the half life of radium is 1690 years. if 70 grams are present now, how much will be present in 450 years?**

---------

A(450) = 70*(1/2)^(450/1690) = 70*0.83 = 58.2 grams

*The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73% of the carbon-14 expected in living matter, when did the tree die? The tree died about ______ years ago?*

**formula is:** ** where:** ** = future amount** ** = present amount** **= constant of proportion.** ** = time**

half life of carbon is given by the equation:** because:**

half life of carbon is ** years.**

solve for ** and then you can solve the problem.**

take log of both sides of equation of ** to get:**

this becomes:

divide both sides of this equation by ** to get:**

**solve for ****to get:** ** which becomes:**

if the tree has only **%=**** of the carbon left, then your equation of:** ** becomes:** ** which becomes:**

take the log of both sides of this equation to get:** which becomes:**

divide both sides of this equation by ** to get:**

solve for ** to get:** ** years**

Then round to the nearest whole number:** years**

After the release of radioactive material into the atmosphere from a nuclear power plant in a country in

19821982,

the hay in that country was contaminated by a radioactive isotope (half-life

88

days). If it is safe to feed the hay to cows when

1212%

of the radioactive isotope remains, how long did the farmers need to wait to use this hay?

The population of a colony of mosquitoes obeys the law of uninhibited growth. Use this information to answer parts (a) through (c).

(a) If N is the population of the colony and t is the time in days, express N as a function of t. Consider

Upper N 0N0

is the original amount at

tequals=0

and

knot equals≠0

is a constant that represents the growth rate.

N(t)equals=nothing(Type

an expression using t as the variable and in terms of

*e*.)

(b) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are

14001400

after 1 day, what is the size of the colony after

22

days?

Approximately

nothing

mosquitoes.

(Do not round until the final answer. Then round to the nearest whole number as needed.)

(c) How long is it until there are

50 comma 00050,000

mosquitoes?

About

nothing

days.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

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