Question

Suppose a population P(t) satisfies dP/dt = 0.8P − 0.001P2    P(0) = 50 where t is measured...

Suppose a population P(t) satisfies

dP/dt = 0.8P − 0.001P2    P(0) = 50

where t is measured in years.

(a) What is the carrying capacity?

______

(b) What is P'(0)?

P'(0) = ______

(c) When will the population reach 50% of the carrying capacity? (Round your answer to two decimal places.)
_____yr

Please show all work neatly, line by line, and justify steps so that I can learn.

Thank you!

Math   Calculus   
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