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put this solution on YOUR website!Exponential functions model both phenomena that grow and phenomena that decay.
The general form for the exponential function is:
b is called the base.
For growth phenomena, the base,
For decay phenomena, the base,
A typical example of exponential grow is the increase in money deposited in savings account.
For example, if you deposited $500 at 5% interest per year, how much would you have at the end of 4 years?
The formula is:
where:
A = the amount you would have at the end of 4 years..
P = the principal (amount invested).
r = the rate of interest, in decimal form.
t = the length of time deposited, in years.
In our example, P = $500, r = 0.05, and t = 4 years.
Use your calculator to get the approximate value of
You would have $607.75 in 4 years.
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A typical example of exponential decay is the decrease of radio-active material (radio-active decay) after a length of time.
The term "half-life" is used to indicate the length of time it takes for radio-active material to lose half of its mass.
For example:
The half-life of an isotope of thorium, thorium-234, is 25 days.
If you started with 50 grams of thorium- 234, how much would be left after 100 days?
Since the amount of thorium-234 decreases 50% every 25 days, the exponential function for the decay is:
where t = the number of half-lives that have elapsed. Notice that the base (b = 0.5) is less than 1.
half-lives.
grams.
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