ossidianaZ

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 $f\left(x\right)=13.017{\left(1.05\right)}^{x}$

BleabyinfibiaG

Skilled2021-08-12Added 118 answers

Step 1

The given model is$f\left(x\right)=13.017{\left(1.05\right)}^{x}$

Where x is the number of years since 2006 and$=f\left(x\right)$ is the cost in dollars.

From the table, the average annual cost in 2006 is$\mathrm{\$}12.837.}$

After x years the 2006 will be doubled

So, After x years, the cost will be$2\times 12837=\mathrm{\$}25674}$

Hence,$f\left(x\right)=13.017{\left(1.05\right)}^{x}=25674$

$\left(1.05\right)}^{x}=\frac{25674}{13017$

Taking natural logarithm on each side

$\mathrm{ln}\left(1.05\right)}^{x}=\mathrm{ln}\frac{25674}{13017$

Using calculator,$x\left(\mathrm{ln}1.05\right)=0.679$

Divide by$\mathrm{ln}1.05,\text{}x=\frac{0.679}{\mathrm{ln}1.05}$

Using calculator,$x=13.92$

Rounded off to nearest tens,$x\approx 13$

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.

The given model is

Where x is the number of years since 2006 and

From the table, the average annual cost in 2006 is

After x years the 2006 will be doubled

So, After x years, the cost will be

Hence,

Taking natural logarithm on each side

Using calculator,

Divide by

Using calculator,

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

Final statement:

Hence, based on this model the 2006 cost will be doublend in 2019.

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