|APPLICATIONS OF EXPONENTIAL|
DECAY WORD PROBLEMS:
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Since the population is declining, you know that the growth factor is negative and is called the decay factor or the decay constant. Since we are assuming an exponential model, it means that an exponential equation will describe the size of the population at any time between 1945 and 1996. The generic population model is
We need to solve for the value of a and the value of b.
We started examining the population size in 1945, so let t=0 in 1945. This means that when t=0, the population size was 120,000. A mathematical way of saying this is , Substitute these values in the above equation.
The equation can now be rewritten as
We know that in 1996 ( t=1996-1945=51), the population was 65,000. A mathematical way of saying this is
Let's solve for b.
Take the natural logarithm of both sides of the equation.
The equation describing the population size at any years between 1945 and 1996 is
In 1960, t=1960-1945=15. To find the population in 1960, simply substitute 15 for t in the above equation.
The population in 1960 was about 100,200.
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