Applications of Exponential & Log Function Derivatives
1. The number of bacteria, N, in a certain culture grows exponentially according to: N = 10,000e0.1t where t is in hours.What is the rate of population increase at a) t = 0?
b) t = 100?
Solution: What is known? What are we looking for? Write this in mathematical terms.
N = 10,000e0.1t and dN/dt = ? when t = 0 and t = 100.
How do we get dN/dt?
We take the derivative of N(t) with respect to time.
dN/dt = (0.1)*10,000e0.1t = 1000e0.1t
Then dN/dt (t = 0) = 1000bacteria/hr
dN/dt (t = 100) = 2.20 x 107 bacteria/hr
Wow! Makes you want to go and wash your hands!