Practice Saturation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Saturation is the phenomenon where a growing quantity approaches a limiting value asymptotically, with the rate of growth decreasing as the limit is approached.
Room fills until no more people fit. Growth can't continue forever.
Example 1
mediumThe logistic function P(t) = \dfrac{1000}{1+e^{-0.5(t-6)}} models population growth. Find P(0), P(6), and \lim_{t\to\infty}P(t).
Example 2
hardIdentify the four parameters L, k, x_0 in f(x) = \dfrac{200}{1+9e^{-0.4x}} and describe the qualitative behavior of f.
Example 3
easyFor f(x) = \dfrac{50}{1+e^{-x}}, state the saturation level and the value at x=0. What does the saturation represent physically?
Example 4
mediumA bacteria culture saturates at 10^6 cells. At time t=0 there are 10^4 cells. Write a logistic model P(t) with growth rate k=0.3 per hour and find P(10).