When the runner is halfway to first base, the triangle formed by his position and the first and second bases is a right triangle with legs of 45 ft and 90 ft. The angle between the runner's direction and the line from his position to 2nd base is ...
angle = arctan(90/45) ≈ 63.43°
The "speed made good" in the direction of 2nd base is the product of the cosine of this angle and the runner's speed toward first.
f(x) = 1.8x is a linear function and does not model the growth of bacteria. Perhaps you meant f(x) = 1.8^x, which is an exponential function whose initial value is 1. Please ensure that you have copied down this problem exactly as it was presented.
