To find: The year in which the 2006 cost of

ossidianaZ

ossidianaZ

Answered question

2021-08-11

To find: The year in which the 2006 cost of tution, room and board fees in public colleges will be doubled using the function f(x)=13.017(1.05)x

Answer & Explanation

BleabyinfibiaG

BleabyinfibiaG

Skilled2021-08-12Added 118 answers

Step 1
The given model is f(x)=13.017(1.05)x
Where x is the number of years since 2006 and =f(x) is the cost in dollars.
From the table, the average annual cost in 2006 is $12.837.
After x years the 2006 will be doubled
So, After x years, 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(ln1.05)=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 doublend in 2019.

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