Chapter 4.5, Problem 38E

(a)

To determine

To write: An equation to model this situation if the cards are worth $81.58.

Answer to Problem 38E

  $6x^4+18x^3+24x^2+18x=81.58$

Explanation of Solution

Given information: Investments: Instead of investing in the stock market, many people invest in collections, like baseball cards. Each year, Anna uses some of the money she receives for her birthday to buy one special baseball card. For the last four birthdays, she purchased cards for $6, $18, $24 and $18. The current value of these cards is modeled by $T\left(x\right)=6x^4+18x^3+24x^2+18x,$ where x represents the average rate of return plus one.

  

Calculation:

Set the function equal to the desired value,

  $6x^4+18x^3+24x^2+18x=81.58$

(b)

To determine

To find: The value of x .

Answer to Problem 38E

Approximately 1.1

Explanation of Solution

Given information: Investments: Instead of investing in the stock market, many people invest in collections, like baseball cards. Each year, Anna uses some of the money she receives for her birthday to buy one special baseball card. For the last four birthdays, she purchased cards for $6, $18, $24 and $18. The current value of these cards is modeled by $T\left(x\right)=6x^4+18x^3+24x^2+18x,$ where x represents the average rate of return plus one.

  

Calculation:

  

  $\begin{array}{l}6x^4+18x^3+24x^2+18x=81.58\\ 6x^4+18x^3+24x^2+18x-81.58=0\end{array}$

Approximately 1.1

(c)

To determine

To find: The average rate or return on Anna’s investments.

Answer to Problem 38E

Average rate $=0.1\text{ or }10\text{ percent}$

Explanation of Solution

Given information: Investments: Instead of investing in the stock market, many people invest in collections, like baseball cards. Each year, Anna uses some of the money she receives for her birthday to buy one special baseball card. For the last four birthdays, she purchased cards for $6, $18, $24 and $18. The current value of these cards is modeled by $T\left(x\right)=6x^4+18x^3+24x^2+18x,$ where x represents the average rate of return plus one.

  

Calculation:

At the end of the problem it says x represents the average rate of return plus 1.

So: $\text{Avg}\text{. Rate}+1=x$

  $\text{Avg}\text{. Rate}+1=1.1$

Average Rate = 0.1 or 10 percent.