14. A common use of transformations is to take the units used in one model and c
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Question
14. A common use of transformations is to take the units used in one model and change them to other units. For example, suppose that we have a function, f (x), that models a company's profits in hundreds of thousands of dollars in terms of hundreds of units produced, a. (a) Use transformations to find the function that will give the profits as (b) Use transformations to find the function that will give the profits in (c) Use transformations to find the function that will give the profits in hundreds of thousands of dollars in terms of units produced. millions of dollars in terms of hundreds of units produced. dollars in terms of thousands of units produced. 3.6. COMBINING FUNCTIONS: COMPLICATED BUSINESS, SCIENCE, AND MORE33S (d) What would the units be for the function 5f(a/20)?Explanation / Answer
ANSWER:
f(x) is a function that models a company's profits in hundrends of thousands of dollars in terms of hundreds of units produced;
This means that f(x) is in terms of hundreds of thousands of dollards and 'x' is in terms of hundreds of units produced.
Now we are to find a function that will give the profits as hundreds of thousands of dollars in terms of units produced.
So 'x' which is in hundreds of units produced is to be broken down into single units produced;
Let number of units be = t;
We know that x=100 t
f(t) = f(100x)
So replace 'x' in f(x) equation with 100 't' and you will have an equation f(t) that gives profits in hundreds of thousands of dollars in terms of the number of unit sproduced 't'
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