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A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t)=(493)4 ^1/2, where t represents the number of years from the time of introduction. What is the quadrupling-time for this population of deer?

Sagot :

Answer:

The answer is "2 years".

Step-by-step explanation:

Given:

[tex]\to P(t) = 493\times4^{\frac{t}{2}}[/tex]

when t=0

[tex]P(0) = 493\times4^{\frac{0}{2}}\\\\[/tex]

        [tex]= 493\times4^0\\\\= 493\times 1\\\\= 493 \\[/tex]

 Calculating the quadrupling time:    

[tex]\to P(t) = 4 \times P(0) \\\\[/tex]

            [tex]= 4\times 493 \\\\= 1972[/tex]

 Solving  

[tex]\to 1972= 493\times4^{\frac{t}{2}} \\\\\to 4 = 4^{\frac{t}{2}}\\\\\to \frac{t}{2} = 1\\\\\to t = 2\ years \\\\[/tex]

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