Chapter 9.9, Problem 5CYU

(a)

To determine

To calculate: To make a table showing the amount of money spent after the park has been open $1,2,3,4$ years.

Answer to Problem 5CYU

Table is

Number of years after 2005	Amount of money
1	13.44
2	15.0528
3	16.859136
4	18.88223232

Explanation of Solution

Given information: The amount of money spent at an amusement park continues to increase. The total $T\left(x\right)$ in millions of dollars can be estimated by the function $T\left(x\right)=12{\left(1.12\right)}^x$ , where $x$ is the number of years after it opened in $2005$

Calculation:

Given that the total $T\left(x\right)$ in millions of dollars can be estimated by the function $T\left(x\right)=12{\left(1.12\right)}^x$ , where $x$ is the number of years after it opened in $2005$

When $x=1$

  $\begin{array}{l}T\left(1\right)=12{\left(1.12\right)}^1\\ T\left(1\right)=12\left(1.12\right)\\ T\left(1\right)=13.44\end{array}$

When $x=2$

  $\begin{array}{l}T\left(2\right)=12{\left(1.12\right)}^2\\ T\left(2\right)=12\left(1.2544\right)\\ T\left(2\right)=15.0528\end{array}$

When $x=3$

  $\begin{array}{l}T\left(3\right)=12{\left(1.12\right)}^3\\ T\left(3\right)=12\left(1.404928\right)\\ T\left(3\right)=16.859136\end{array}$

When $x=4$

  $\begin{array}{l}T\left(4\right)=12{\left(1.12\right)}^4\\ T\left(4\right)=12\left(1.57351936\right)\\ T\left(4\right)=18.88223232\end{array}$

Thus, table is

Number of years after 2005	Amount of money
1	13.44
2	15.0528
3	16.859136
4	18.88223232

Conclusion:

Hence, table is created

(b)

To determine

To calculate: To graph the function

Explanation of Solution

Given information: The amount of money spent at an amusement park continues to increase. The total $T\left(x\right)$ in millions of dollars can be estimated by the function $T\left(x\right)=12{\left(1.12\right)}^x$ , where $x$ is the number of years after it opened in $2005$

Calculation:

Given that the total $T\left(x\right)$ in millions of dollars can be estimated by the function $T\left(x\right)=12{\left(1.12\right)}^x$ , where $x$ is the number of years after it opened in $2005$

Thus, table is

Number of years after 2005	Amount of money
1	13.44
2	15.0528
3	16.859136
4	18.88223232

Plotting the points on graph:

  

Conclusion:

Hence, graph is sketched

(c)

To determine

To calculate: To find what does the y-intercept represent

Answer to Problem 5CYU

y-intercept represents the amount of money spent at an amusement park in the year $2005$

Explanation of Solution

Given information: The amount of money spent at an amusement park continues to increase. The total $T\left(x\right)$ in millions of dollars can be estimated by the function $T\left(x\right)=12{\left(1.12\right)}^x$ , where $x$ is the number of years after it opened in $2005$

Calculation:

Given that the total $T\left(x\right)$ in millions of dollars can be estimated by the function $T\left(x\right)=12{\left(1.12\right)}^x$ , where $x$ is the number of years after it opened in $2005$

Graph is as follows:

  

Here, y-intercept represents the amount of money spent at an amusement park in the year $2005$

Conclusion:

Hence, y-intercept represents the amount of money spent at an amusement park in the year $2005$