Final answer:
To find the equation of the tangent line to s(t) = 16 - t at t = 0, calculate the derivative (slope) which is -1 and evaluate s(0) to find the y-intercept. The equation is y = -x + 16.
Step-by-step explanation:
The equation of the tangent line to the function s(t) = 16 - t when t = 0 can be found by using the derivative. In this case, the function is linear, so its derivative, which is the slope of the tangent line, is constant. Therefore, the derivative of s(t) with respect to t is -1, as the coefficient of t is -1.
Since we are looking for the tangent line at t = 0, we shall evaluate the function s at t = 0, which yields s(0) = 16. Thus, the equation of the tangent line is y = -1x + 16, or simply y = -x + 16.