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A certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the population will grow to P(t)=(177)4^t/2, where t represents the number of years from the time of introduction. What is the doubling-time for this population of alligators?

Respuesta :

pedrocarratore

Answer:

1 year

Step-by-step explanation:

The population as a function of time is:

[tex]P(t)  =177*4^{\frac{t}{2}}[/tex]

First, find the initial population at t=0:

[tex]P(0)  =177*4^{\frac{0}{2}}\\P(0) = 177[/tex]

Then, double it:

[tex]2P(0) = 2*177 = 354[/tex]

Finally, find the value of 't' for which the population is 354:

[tex]354  =177*4^{\frac{t}{2}}\\4^{\frac{t}{2}}=2\\log(4^{\frac{t}{2}})=log(2)\\\frac{t}{2} *log(4) = log(2)\\t=2*\frac{log(2)}{log(4)}\\t=1[/tex]

The alligator population will double afer 1 year.

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