The percent `p` of a popuation that has completed 4 years of college is given by the function `p(t) = -0.001 t^2 + 0.4 t` . Where t represents time , in years . What percent of the population has completed four years of college after 20 years , to the nearest tenth ?

Options

A. `0.1`
B. `7.6`
C. `8.0`
D. `8.4`

Answer

To find the percent \( p \) of a population that has completed 4 years of college after 20 years, we will use the function given:

\[ p(t) = -0.001 t^2 + 0.4 t \]

where \( t \) represents time in years. We need to evaluate this function at \( t = 20 \).

### Step-by-Step Solution:

1. **Substitute \( t = 20 \) into the function**:
\[ p(20) = -0.001(20^2) + 0.4(20) \]

2. **Calculate \( 20^2 \)**:
\[ 20^2 = 400 \]

3. **Substitute \( 400 \) back into the equation**:
\[ p(20) = -0.001(400) + 0.4(20) \]

4. **Calculate \( -0.001 \times 400 \)**:
\[ -0.001 \times 400 = -0.4 \]

5. **Calculate \( 0.4 \times 20 \)**:
\[ 0.4 \times 20 = 8 \]

6. **Combine the results**:
\[ p(20) = -0.4 + 8 \]

7. **Final calculation**:
\[ p(20) = 7.6 \]

Thus, the percent of the population that has completed 4 years of college after 20 years is **7.6%**.