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
Answered question
2021-02-03
Answer & Explanation
odgovoreh
Skilled2021-02-04Added 107 answers
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
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
Hence,
Taking natural logarithm on each side
Using calculator,
Divide by
Using calculator, x = 13.92
Rounded off to nearest tens,
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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