## Related questions with answers

The number of pages in the IRS Tax Code has increased from $400$ pages in 1913 to $70,320$ pages in 2009. The increase can be modeled by the exponential function

$T(x)=400(1.055)^x,$

where $x$ is the number of years since 1913. Use this function to estimate the number of pages in the tax code for 1950, 1990, and for 2000. Round to the nearest one.

Solution

VerifiedBy substituting in the function

$\begin{aligned} T\left(x\right)=400\cdot\left(1.055\right)^x \end{aligned}$

, for the values $x=37,77$, and $x=87$, respectively, where $x$ represents the number of years since $1913$, the following is true:

$\begin{aligned} T\left(\textcolor{#4257b2}{37}\right)&=400\cdot\left(1.055\right)^{\textcolor{#4257b2}{37}}\\ &=400\cdot7.25\\ &=2,900\\ T\left(\textcolor{#4257b2}{77}\right)&=400\cdot\left(1.055\right)^{\textcolor{#4257b2}{77}}\\ &=400\cdot61.721915\\ &=24,688.766\\ &\approx24,689\\ T\left(\textcolor{#4257b2}{87}\right)&=400\cdot\left(1.055\right)^{\textcolor{#4257b2}{87}}\\ &=400\cdot105.429947\\ &=42,171.9788\\ &\approx42,172 \end{aligned}$

Therefore, the number of pages in the tax code for $1950$ was $2,900$ pages, for $1990$ was $24,689$ pages, and for $2000$ was $42,172$ pages.

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