Chapter 8, Problem 49CR

(a)

To determine

To find: The formula for the nth term of the geometric sequence that gives the value of the fleet $n$ full years after it was purchased.

Answer to Problem 49CR

Therequired formula is $a_n=\$130000{\left(0.7\right)}^t$ .

Explanation of Solution

Given:

The cost of 6 vans is $\$130000$ .

The depreciation rate is $30\%$ per year during the next 5 years.

Calculation:

Consider the first term and the common ratio of the sequence is,

  $\begin{array}{l}{a}_1=\$130000\\ r=70\%\end{array}$

The, formula for the nth term of the arithmetic sequence is,

  $a_n=a_1{r}^{n-1}$

Then,

  $a_n=\$130000{\left(0.7\right)}^t$

(b)

To determine

To find: The depreciated value of the fleet at the end of 5 year.

Answer to Problem 49CR

The value at the end of the 5 years is $\$21849.10$ .

Explanation of Solution

Given:

The cost of 6 vans is $\$130000$ .

The depreciation rate is $30\%$ per year during the next 5 years.

Calculation:

Consider the formula for the model is,

  $a_n=\$130000{\left(0.7\right)}^t$

Then, the value at the end of 5 years is,

  $\begin{array}{c}{a}_n=\$130000{\left(0.7\right)}^5\\ =\$21849.10\end{array}$

Thus, the value at the end of the 5 years is $\$21849.10$ .