SOLUTION: How do I set up this problem, there were 1.388 millions childcare workers in 2006. The number of job opportunities in that fieldis expected to grow to 1.636 million by 2016. What i

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Question 503855: How do I set up this problem, there were 1.388 millions childcare workers in 2006. The number of job opportunities in that fieldis expected to grow to 1.636 million by 2016. What is the percent of increase?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
today there are 1.388 million childcare workers in 2006
there will be 1.636 million by 2016.
what is the percent increase?
the number of years is equal to 2016 - 2006 = 10 years.
the equation to find the percent increase per year is:
f = p * (1+x)^n
f = the future number of workers
p = the present number of workers
x = the annual increase
n = the number of years
we have:
f = 1.636 million
p = 1.388 million
n = 10
x = what we want to find.
the formula becomes:
1.636 = 1.388 * (1+x)^10
divide both sides of the equation by 1.388 to get:
1.636 / 1.388 = (1+x)^10
simplify to get:
1.178674352 = (1+x)^10
take the tenth root of both sides of the equation to get:
1.178674352^(1/10) = ((1+x)^10)^(1/10)
simplify to get:
1.016574902 = 1+x
subtract 1 from both sides of the equation to get:
.016574902 = x
x is the interest rate.
to get the percent, multiply the rate by 100% to get:
interest rate = 1.6574902% per year.

Answer by ikleyn(52860) About Me  (Show Source):
You can put this solution on YOUR website!
.
How do I set up this problem, there were 1.388 millions childcare workers in 2006.
The number of job opportunities in that field is expected to grow to 1.636 million by 2016.
What is the percent of increase?
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        Tutor @Theo incorrectly reads the problem and incorrectly treats it.
        His solution is irrelevant, and his answer is incorrect. 


They ask about the percentage of change between the new value and the old value.


The standard formula for it is

                             new value - old value
    the percent of change = ------------------------ x 100.
                                old value



As we apply it with the numbers, we get


    the percent of change =  %281.636-1.388%29%2F1.388%29%2A100 = 17.867  (approximately).


What you need to know:


    (a)  if not said explicitly, divide by the old value, by default;

    (b)  multiply the ratio by 100 to transform the ratio's value to the percentage value.

Solved.