7 3 B Applications of Solving Exponential Equations

7. 3 B Applications of Solving Exponential Equations a is the initial amount b is the growth factor t is time (years, months, days, hours) p is the time for one period Math 30 -1 1

Application of Exponential Growth A cell doubles every 4 min. If there are 500 cells originally, how much time would pass when they reached 16 000 cells? Therefore, it would take 20 min for the cells to reach 16 000. t = 20 Math 30 -1 2

Applications of Exponential Equations Radioactive materials decay in an exponential manner. If Radon has a half life of 25 days, how long would it take a 200 mg sample to decay to 12. 5 mg? It takes 100 days for the sample to decay to 12. 5 mg. Math 30 -1 3

Applications of Exponential Equations A bacterial culture doubles in size every 25 minutes. If a population starts with 100 bacteria, then how long will it take the population to reach 1 638 400? It would take the bacteria 350 minutes or approximately 5. 83 hours to reach a population of 1 638 400. Math 30 -1 4

Applications of Exponential Equations Cobalt-60 which has a half-life of 5. 3 years, is used extensively in medical radiology. The amount left at any given time is given by: a) What fraction of the initial amount will be left after 15. 9 years? b) How long will it take until there is only 6. 25% of the original amount left? Math 30 -1 5

If S 4000 is invested in an account paying 0. 03% daily interest compounded daily, what is the balance after 7 years? Determine how long $1000 needs to be invested in an account that earns 8. 3% per year, compounded semi-annually before it increases in value to $1490. Math 30 -1 Must round to 5 years 6

Assignment Page 364 8, 9, 10, 11, 12, 13, 14 Math 30 -1 7