The following table gives the ​distance f(t) fallen by a smoke jumper seconds after she opens her chute​. <IMAGE>
a. Use the forward difference quotient with ℎ = 0.5 to estimate the velocity of the smoke jumper at t=2 seconds.

Verified step by step guidance

1. Step 1: Understand the forward difference quotient. The forward difference quotient is a method to estimate the derivative of a function at a certain point. It is given by the formula: \( f'(t) \approx \frac{f(t+h) - f(t)}{h} \), where \( h \) is a small increment.
2. Step 2: Identify the values needed from the table. You need the distance \( f(t) \) at \( t = 2 \) seconds and \( f(t+h) \) at \( t = 2.5 \) seconds, since \( h = 0.5 \).
3. Step 3: Substitute the values into the forward difference quotient formula. Use the values from the table for \( f(2) \) and \( f(2.5) \) to calculate the approximate velocity.
4. Step 4: Calculate the difference in distances. Find \( f(2.5) - f(2) \) to determine how much the distance has changed over the interval from \( t = 2 \) to \( t = 2.5 \).
5. Step 5: Divide the difference by \( h = 0.5 \). This will give you the estimated velocity of the smoke jumper at \( t = 2 \) seconds.