1. **State the problem:** We are given the speed function of a model car as $$v(t) = 16 - 10t^2$$ for $$0 \leq t \leq 6$$ seconds. We need to fill in the missing values in the table for specific times and then draw the graph of $$y = v(t)$$. 2. **Recall the formula:** The speed at time $$t$$ is given by $$v(t) = 16 - 10t^2$$. 3. **Calculate missing values:** - For $$t=0$$: $$v(0) = 16 - 10 \times 0^2 = 16 - 0 = 16$$ - For $$t=1$$: Given as 9.9 (approximate) - For $$t=2$$: $$v(2) = 16 - 10 \times 2^2 = 16 - 10 \times 4 = 16 - 40 = -24$$ - For $$t=3$$: $$v(3) = 16 - 10 \times 3^2 = 16 - 90 = -74$$ - For $$t=4$$: Given as 14.6 (approximate) but let's verify: $$v(4) = 16 - 10 \times 4^2 = 16 - 160 = -144$$ (Given value 14.6 is inconsistent with formula, so we trust formula) - For $$t=5$$: $$v(5) = 16 - 10 \times 25 = 16 - 250 = -234$$ - For $$t=6$$: Given as 15.5 (approximate) but formula gives: $$v(6) = 16 - 10 \times 36 = 16 - 360 = -344$$ 4. **Fill in the table with correct values rounded to 1 decimal place:** | Time, t (secs) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |----------------|-----|-----|------|------|-------|-------|-------| | Speed, v (m/s) | 16.0| 6.0 | -24.0| -74.0| -144.0| -234.0| -344.0| 5. **Explanation:** The given values in the table for $$t=1,4,6$$ do not match the function formula. We rely on the formula to calculate the correct speeds. 6. **Graph description:** The graph of $$y = v(t)$$ is a downward opening parabola starting at $$v(0) = 16$$ and decreasing rapidly as $$t$$ increases. The speed becomes negative after $$t=1.26$$ approximately, indicating the model car slows down and reverses direction if negative speed is physically meaningful. 7. **Desmos function for graphing:** $$y = 16 - 10t^2$$ for $$0 \leq t \leq 6$$. Final answer: The completed table values are as above, and the graph is a parabola described by $$y = 16 - 10t^2$$.