The customer service department of a wireless cellular provider has found that on Wednesdays, the polynomial funciton `C (t)=-0.0815t ^(4)+t ^(3)+12t` approximates the number of calls received by any given time, where t represents the number of hours that have passed during the workday. Based on this function, how many calls can be expected by the end of one 10-hour workday ?

Explanation

To find the expected number of calls received by the end of a 10-hour workday using the polynomial function \( C(t) = -0.0815t^4 + t^3 + 12t \), we will substitute \( t = 10 \) into the function and calculate the result step by step.

### Step-by-Step Solution:

1. **Write down the function**:
\[ C(t) = -0.0815t^4 + t^3 + 12t \]

2. **Substitute \( t = 10 \)**:
\[ C(10) = -0.0815(10)^4 + (10)^3 + 12(10) \]

3. **Calculate \( (10)^4 \)**:
\[ (10)^4 = 10000 \]

4. **Calculate \( (10)^3 \)**:
\[ (10)^3 = 1000 \]

5. **Calculate \( 12(10) \)**:
\[ 12(10) = 120 \]

6. **Substitute these values back into the equation**:
\[ C(10) = -0.0815(10000) + 1000 + 120 \]

7. **Calculate \( -0.0815 \times 10000 \)**:
\[ -0.0815 \times 10000 = -815 \]

8. **Combine all the terms**:
\[ C(10) = -815 + 1000 + 120 \]

9. **Perform the addition**:
\[ C(10) = -815 + 1120 = 305 \]

10. **Final Result**:
\[ C(10) = 305 \]

Thus, the expected number of calls by the end of a 10-hour workday is **305**.