Question 1181198
Here's how to determine the function for the book value and calculate the book value after 8 and 11.5 years:

**a) Determine the function V = f(t):**

1. **Calculate the annual depreciation:**

*   Depreciable amount = Purchase price - Salvage value
*   Depreciable amount = $1,000,000 - $123,000 = $877,000
*   Annual depreciation = Depreciable amount / Useful life
*   Annual depreciation = $877,000 / 12 years = $73,083.33 per year (approximately)

2. **Write the function:**

Since we're using straight-line depreciation, the book value decreases linearly over time.  The function will be in the form:

V(t) = Initial book value - (Annual depreciation * t)

V(t) = $1,000,000 - $73,083.33t

**b) Determine the book value after 8 years and 11.5 years:**

Using the function V(t) = $1,000,000 - $73,083.33t:

*   **After 8 years:**
    V(8) = $1,000,000 - ($73,083.33 * 8)
    V(8) = $1,000,000 - $584,666.64
    V(8) = $415,333.36

*   **After 11.5 years:**
    V(11.5) = $1,000,000 - ($73,083.33 * 11.5)
    V(11.5) = $1,000,000 - $840,458.295
    V(11.5) = $159,541.705

**Answers:**

*   a) The function V = f(t) is:  V(t) = $1,000,000 - $73,083.33t
*   b) The book value after 8 years is approximately $415,333.36.
*   b) The book value after 11.5 years is approximately $159,541.71.