Question

The number of points a race car driver earns depends on the place that they finish in the race. The sequence below represents the number of points that a driver earns. 44, 42, 40, 38, ... Which explicit formula can be used to determine the number of points the racer who finished in nth place will earn? A. P(n) = 44 – 2n B. P(n) = 46 – 2n C. P(n) = n – 2 D. P(n) = 44n – 2

Answer 1

The explicit formula to determine the number of points a racer earning in nth place is P(n) = 46 - 2n, starting from n=1, reflecting the linear decrease of points with each subsequent place.

Step-by-step explanation:

To determine the number of points a racer who finished in nth place will earn, we need to find an explicit formula based on the given sequence: 44, 42, 40, 38, ... Each term decreases by 2, indicating a linear relationship between the place finished and the points earned.

The correct formula to calculate the points P(n) for the nth place is P(n) = 46 - 2n. This is because the first place finishes with 44 points (which is the second term if we use our formula starting from n=1), so the initial value when n=1 should be 46, and then we subtract twice the place number to account for the decrease by 2 points for each subsequent place.

Here is the step-by-step breakdown:

1. Start with the initial value of points for the first place, which is 44.
2. Observe that each subsequent place earns 2 points less, suggesting a subtraction of 2 points per rank increase.
3. Adjust for the fact that the formula starts with n=1, so we add 2 to the initial value to get 46.
4. Combine these observations into the formula: P(n) = 46 - 2n.