Try the fastest way to create flashcards
Question

# 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

Verified
Step 1
1 of 2

By 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.

## Recommended textbook solutions

#### College Algebra and Trigonometry

1st EditionISBN: 9780078035623Donna Gerken, Julie Miller
9,697 solutions

#### College Algebra: Graphs and Models

5th EditionISBN: 9780321783950 (3 more)Bittinger, Ellenbogen, Judith A. Beecher, Judith A. Penna
5,779 solutions

#### Algebra and Trigonometry

4th EditionISBN: 9781305071742 (3 more)Lothar Redlin, Stewart, Watson
11,356 solutions

#### College Algebra and Trigonometry

7th EditionISBN: 9781439048603Richard D. Nation, Richard N. Aufmann, Vernon C. Barker
7,752 solutions