- The function \(f(x) = 4x + 10\) relates hours worked to earnings.
- Substitute \(x = 2\) into the equation to find total earnings.
- Perform the arithmetic calculation: \(f(2) = 4(2) + 10 = 18\).
- The final result is \(\boxed{18}\), which matches option D.
Explanation
- Understanding the Problem
The problem asks to calculate the amount of money earned by Francis babysitting for \(2\) hours based on the function \(f(x) = 4x + 10\). In this model, \(f(x)\) represents the total earnings in dollars, and \(x\) represents the time spent working in hours. To find the amount earned for \(2\) hours of work, we need to evaluate the function \(f(x)\) at \(x = 2\).
- Evaluating the Function
We substitute the value \(x = 2\) into the given function \(f(x) = 4x + 10\):
\[f(2) = 4(2) + 10\]
Performing the multiplication first:
\[4 \times 2 = 8\]
Then, adding the constant:
\[8 + 10 = 18\]
Therefore, the amount of money earned by Francis for \(2\) hours of work is \(\$18\). Comparing this result with the given options, it corresponds to option D.
Examples
This type of linear function modeling is very common in everyday life, such as calculating wages based on an hourly rate. For example, if a ride-sharing app charges a base fee of \(\$5\) plus \(\$2\) per mile, the total cost \(C\) for a trip of \(d\) miles can be modeled by \(C(d) = 2d + 5\). By understanding how to substitute and evaluate these functions, you can easily predict costs or earnings in various real-world situations.