Write a real world situation for the function f(x) = 3(1.06x) + 2. Be sure to identify all key features of the function as what they represent in your situation.

Sure, let's consider a real-world situation for the function f(x) = 3(1.06x) + 2.

Example Situation:

In this scenario, let's say you and your friends are planning to go on a road trip. The function f(x) represents the total cost of the road trip, where x represents the distance that you plan to travel.

Key Features:

1. f(x): This represents the total cost of the road trip. It tells us how much money you need to budget for the trip.

2. 3: This is the coefficient of (1.06x). It indicates that for every unit of distance traveled (x), the cost increases by a factor of 3. So, the cost of the trip is multiplied by 3 for every unit of distance.

3. 1.06: This is the multiplier for x. It represents a 6% increase in the cost for each unit of distance. This accounts for additional expenses like fuel, tolls, or activities along the way.

4. 2: This term represents a constant value of $2. It accounts for any fixed costs that may be associated with the road trip, such as parking fees or road trip essentials.

To find the cost of the road trip for a specific distance, you need to plug in the value of x into the function f(x).

For example, if you plan to travel a distance of 100 miles, you calculate it as follows:

f(100) = 3(1.06 * 100) + 2
= 3(106) + 2
= 318 + 2
= $320

Therefore, for a 100-mile road trip, the total cost would be $320, considering the given function.