Need help with Exponential Function Word Probs?

Question

Need help doing these, I need the function equations as well

1. Radium-221 has a half-life of 30 seconds. What fraction of a sample would remain after 10 minutes?

2. A bacteria culture doubles every .25 hours. At tune 1.25 hours, an estimate of 40 000 is taken. Calculate the initial size of the culture and the size after 3 hours


3. The half-life of Paladium-100 is 4 days. After 16 days a sample has been reduced to a mass of .75 mg. What is the initial mass of the sample?

--Any contribution would be greatly appreciated! Thanks!

Answer 1

1. After every 30 seconds radium 221 decays to half its original amount.
Let initial amount be x . After n half lives the amount is
(1/2)^n x
Here n = 20
After 10 minutes (1/2)^20 of the sample will remain

This is approximately 10^-6 or 0.0001%

2) Let the initial size be x , after every .25 hours the size is 2x. After n such periods the size is (2)^n x
2^5 x = 40,000
x = 40,000/32 = 1250
Initial size = 1250

Size after 3 hours , no of 0.25 hour periods = 12
size = 2^12 * 1250 = 5,120,000

3)16 days no of half lives = 4
x(1/2) ^ 4 = 0.75
x = 16 * 0.75 = 12 mg
Answer 12 mg

Answer 2

(1) half-life means when will half be gone. so every 30 seconds, you lose 1/2. so after 30 seconds you have half, then after 30 more seconds, you only have half of half.. then after 30 more seconds half-of-half-of half.. so how many times will it half in 10 minutes? 30 seconds = 2 every minute X 10 minutes. so 1/2 X 1/2 X 1/2.. 20 times.. (1/2)^20
1 / 2^20 Formula is (1/2) ^ (time / half life)

The formula you use is y = (1/2) ^ (time/halflife)

Answer 3

1)
10*60=600 seconds
600/30=20 times
answer:
1-[(1/2)+(1/2)^2+(1/2)^3+...+(1/2)^20]