An exponential function multiplies by the same factor each step, like N(d) = 6 × 2ᵈ for the crew's duckweed count. Build it from a table or two points, and rewrite it to read a daily or weekly rate. A geometric sequence is the same idea written term by term, recursively or explicitly. The sum of the first n terms is a(rⁿ - 1)/(r - 1), and you can derive that formula by subtracting r times the sum from the sum.