Math 141, Sem. I, 1998-99 (R.A. Brualdi)
Handout 16 (October 30, 1998)
Topic: Problems on Exponential decay and the like


1. The isotope of hydrogen H^3 (tritium) is radioactive, decaying with a
half-life of 12.6 years. If we start with 500 grams, how much remains after 10
years? After 100 years? 

2. Many pesticides gradually decay in the environment, obeying a similar decay
law as radioactive materials. Carbamate pesticides are often used on vegetable
crops because they decay quickly; typically the half-life is 2.6 days. Suppose
crops are sprayed so that they contain 50 ppm (parts per million) of a
carbamate pesticide. 

(a) If crops are sprayed two weeks before harvest, how much (ppm)  remains at
harvest time? 

(b) If a safe level is regarded as 1 ppm, how long would have to wait until a
safe level is achieved, if the initial level was 50 ppm? 

3. Bacillus Quantitatus grows at a constant percentage rate of 20% per hour. 
It was introduced into a jar at 8 AM Thursday morning (October 29, 1998) At 4
PM on Thursday the bacteria count was 78,000 bacteria per square inch. 

(a) What was the bacteria count at noon on Thursday?

(b) What was it this morning (Friday) at 8 AM?

(c) At 10 AM today (Friday), after class, I plan to introduce a toxic
substance into the jar which has the effect of stopping the growth and
reducing the count of Bacillus Quantitatus in the jar at the rate of 5% per
hour.

     (i) When is the count equal to 150,000 bacteria per square inch?

     (ii) When is the count back down to 78,000 bacteria per square inch?