Problema Solution
A species of animal is discovered on an island. Suppose that the population size P (t) of the species can be modeled by the following exponential function, where time t is measured in years.
P(t)= 400/1+5e^-0.31t
Find the initial population size of the species and the population size after 10 years. Round your answers to the nearest whole number as necessary.
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P(t)= 400/(1+5e^-0.31t)
At initial, t=0,
=> P(0) = 400/(1+5e^0)
=> P(0) = 400/(1+5) = 400/6 = 66.67 = 67 (approx.)
After 10 years
t=10
P(10) = 400/(1+5e^-3.1)
= 400/(1+5(0.045))
= 325.2 = 325 (approx.)