{Use of Tech} Decreasing velocity A projectile is fired upward, and its velocity in m/s is given by v(t) = 200e^−t/10, for t≥0.
a. Graph the velocity function, for t≥0.

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1. Identify the velocity function given in the problem: \( v(t) = 200e^{-t/10} \). This is an exponential decay function, where the velocity decreases over time.
2. Understand the behavior of the function: As \( t \) increases, the term \( e^{-t/10} \) decreases because the exponent is negative, leading to a decrease in \( v(t) \).
3. Determine the initial condition: At \( t = 0 \), the velocity \( v(0) = 200e^{0} = 200 \) m/s. This is the initial velocity of the projectile.
4. Consider the long-term behavior: As \( t \to \infty \), \( e^{-t/10} \to 0 \), so \( v(t) \to 0 \). This means the velocity approaches zero as time goes on.
5. To graph the function, plot \( v(t) \) against \( t \) for \( t \geq 0 \). Start at the point (0, 200) and show the curve decreasing towards zero, illustrating the exponential decay of velocity over time.