1 At the beginning of an experiment a scientist has 140 gram

1. At the beginning of an experiment, a scientist has 140 grams of radioactive goo. After 120 minutes, her sample has decayed to 4.375 grams.

a. What is the half-life of the goo in minutes?

b. Find a formula for G(t), the amount of goo remaining at time t. G(t)=

c. How many grams of goo will remain after 35 minutes?

2. The count in a bateria culture was 500 after 10 minutes and 1600 after 35 minutes. Assuming the count grows exponentially,

a. Find the doubling period.

b. What was the initial size of the culture?

c. Find the population after 90 minutes.

d. When will the population reach 14000.

3. Find the time required for an investment of 5000 dollars to grow to 8000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Solution

1) equation of expoenetial decay :

N= Noe^-kt

4.375 = 140e^-120k

k = 0.0288

a) half life = 0.693/0.0288 = 24.06 min

b) G(t) = 140e^-0.0288t

c) After 35 min: G(35) = 140e^-0.0288*35 = 51.09 gm