Lucy is knitting a blanket and needs to buy some more yarn. At her local craft store, 2 skeins of yarn cost 57 and 8 skeins of y
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Given:
The increase in pressure P is the linear function of the depth d.
The cost of dinner is $300 and $10 per students.
To find:
The initial value and rate of change and their interpretation.
Find the cost function C where n is the number of students.
Solution:
The slope intercept form of a linear function is
...(i)
where, m is rate of change and b is y-intercept or initial value.
We have,
...(ii)
From (i) and (ii), we get
The initial value is 14.7. It means, the pressure at sea level is 14.7 pounds psi.
Rate of change is 0.445. It means, the pressure is increasing by 0.445 pounds psi for every feet.
The cost of dinner is $300 and $10 per students.
Let C(n) be the total cost for dinner and n be the number of students.
Fixed cost = $300
Additional cost for 1 student = $10
Additional cost for n student = $10n
Now,
Total cost = Fixed cost + Additional cost
Therefore, the required cost function is .
We have a domain of a function, that is, which x-es can we throw in. But we are asking which y-s will we get given that we can only throw x-es in .
Let's try even though we are forbidden to put 4 inside
we are still able to do so.
So what we just got is the upper limit of the range. The lower limit is
.
So the range is just .
Hope this helps :)