Many biological populations, both plant and animal, experience seasonal growth. For example, an animal population might flourish during the spring and summer and die back in the fall. The population, ƒ(t), at time t, is often modeled by

where ƒ(0) is the size of the population when t = 0. Suppose that ƒ(0) = 1000 and c = 2. Find the functional values in parts (a)–(d).
(a) ƒ(0.2) 

(b) ƒ(1) 

(c) ƒ′(0) 

(d) ƒ′(0.2)

(e) Use a graphing calculator to graph ƒ(t) on [0, 11].
(f) Find the maximum and minimum values of ƒ(t) and the values of t where they occur.

Transcribed Image Text:

f(t) = f(0)ec sin(1)