To find:The year in which the 2006 cost of tuition, room and board fees in public colleges will be doubled using the function f{{left({x}right)}}={13},{017}{left({1.05}right)}^{x}.

Khadija Wells 2021-02-03 Answered
To find:The year in which the 2006 cost of tuition, room and board fees in public colleges will be doubled using the function f(x)=13,017(1.05)x.
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Expert Answer

odgovoreh
Answered 2021-02-04 Author has 107 answers
Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model is f(x)=13,017(1.05)x
Where x is the number of years since 2006 and y = f(x) is the cost in dollars.
From the table, the average annual cost in 2006 is $12,837.
After xyears the 2006 will be doubled
So, After xyears, the cost will be 2×12837=$25674.
Hence, f(x)=13,017(1.05)x=25674
(1.05)x=2567413017
Taking natural logarithm on each side
ln(1.05)x=ln2567413017
Using calculator, x(In1.05)=0.679
Divide by ln1.05,x=0.679ln1.05
Using calculator, x = 13.92
Rounded off to nearest tens, x13
Hence, based on this model the 2006 cost will be doubled in 13 years since 2006.
That is, the year = 2006+13 = 2019
Final statement:
Hence, based on this model the 2006 cost will be doubled in 2019.
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