7.3b applications of solving exponential equations
DESCRIPTION
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 30-1TRANSCRIPT
Math 30-1 1
7.3B Applications of Solving Exponential Equations
Final Initial ( factor)time
time per period
xy a b tpy a b
a is the initial amountb is the growth factort is time (years, months, days, hours)p is the time for one period
Math 30-1 2
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?
16 000 500 2t4
32 2t4
25 2t4
5 t4
t = 20
Therefore, it would take20 min for the cells toreach 16 000.
Final Initial ( factor)time
time per periodtpy a b
Math 30-1 3
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?
Applications of Exponential Equations
2512
12.5 200
t
2512.5 1200 2
t
251 116 2
t
425t
412 25
t
100t
It takes 100 days for the sample to decay to 12.5 mg.
Final Initial ( factor)time
time per periodtpy a b
Math 30-1 4
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?
Applications of Exponential Equations
251638400 1 0 20t
2516384 2t
14 252 2t
1425t
350t
It would take the bacteria 350 minutes or approximately 5.83 hours to reach a population of 1 638 400.
tpy a b Final Initial ( factor)
timetime per period
Math 30-1 5
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: 3.5
21
t
OAAL 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?
3.59.15
21
OAAL 321
OAAL 81OAAL
5.3120.0625 1
t
5.341 12 2
t
4 5.3t
2.21t
Applications of Exponential Equations
Math 30-1 6
If S4000 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.
tpy a b Final Initial ( factor)
timetime per period
7 36514000 1.0003A
8607.89A
120831490 1000 1
2
t
21.49 1.0415 t
4.9t yearsMust round to 5 years
Math 30-1 7
AssignmentPage 3648, 9, 10, 11, 12, 13, 14