Applications: growth, decay and motion
Differential equations (introductory) · Mathematics
Study notes
Q: A bacteria culture doubles every 3 hours. Starting from 1000, how many after 10 hours? dy/dt = ky, doubling: e^(3k) = 2, k = ln 2 / 3. y = 1000 e^(kt) = 1000 e^((ln 2 / 3)(10)) = 1000 times 2^(10/3). 2^(10/3) = 2^3 times 2^(1/3) = 8 times 1.26 = 10.08. About 10,080 bacteria.