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2 answers:
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Given:
The function is:
Where p(t) represents the number of milligrams of the substance and t represents the time.
To find:
The correct explanation for the number 0.25 and 500 in the given function.
Solution:
The general exponential function is:
...(i)
Where, a is the initial value and b is the growth/decay factor. If , then decay factor and if
, then growth factor.
We have,
...(ii)
On comparing (i) and (ii), we get
, it means initial there are 500 milligrams of the substance.
, this value is less than 1, it means the substance is decreasing by a factor of 0.25.
Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.
Answer:
849 items.
Step-by-step explanation:
Given that the profit C (in thousands of dollars) for x thousands of items related as
As the profit is $14,000 for producing 2000 items, so
C= 14 thousand dollars and
x= 2 thousand items.
Putting C= 14 in the equation ( we have),
Now, x=2 is one of the solutions to the equation (ii), so (x-2) is a factor of the equation (ii), we have
We have the given solution for x-2=0, so sloving -5x^2-4x+7=0 for other solutions.
As the number of items cant be negative, so x= 0.849 thousand is the other number of items.
Hence, the other number of items for the same profit is 849 items.