You are taking a road trip across several states. Your distance from your final destination is modeled with the equation f(x)=-350x+1,400, where x represents the number of days you have traveling. Identify and interpret the initial value.

Question

The initial value of 1,400 represents the distance from your starting point to your final destination.
The initial value of 350 represents the distance you travel each day.
The initial value of 1,400 represents the distance you travel each day.
The initial value of 350 represents the distance from your starting point to your final destination.

Answer 1

The correct interpretation of the initial value in the equation \( f(x) = -350x + 1,400 \) is:

The initial value of 1,400 represents the distance from your starting point to your final destination.

Here's a brief explanation: In this equation, \( f(x) \) indicates the distance remaining (in miles) after traveling \( x \) days. When \( x = 0 \) (the start of your journey), \( f(0) = 1,400 \). This means at the beginning of your trip, you are 1,400 miles away from your final destination.

The coefficient of \( x \), which is -350, indicates that you are traveling 350 miles each day.