Respuesta :
Answer:
The tripling-time for the population of deer is 3 years.
Step-by-step explanation:
Consider the population of deer represented by the function
[tex]P(t)=767(3^{\frac{t}{3}})[/tex]
Substitute t=0 to find the initial population.
[tex]P(0)=767(3^{\frac{0}{3}})=767(3^0)=767(1)=767[/tex]
Initial population is 767.
Population after tripling = [tex]767\times 3[/tex]
[tex]767\times 3=767(3^{\frac{t}{3}})[/tex]
Divide both sides by 767.
[tex]3=3^{\frac{t}{3}}[/tex]
[tex]3^1=3^{\frac{t}{3}}[/tex]
On comparing both sides we get.
[tex]1=\frac{t}{3}[/tex]
[tex]3=t[/tex]
Therefore, the tripling-time for the population of deer is 3 years.
Tripling time means that in how many years population becomes three times.
Tripling time for population of deer is 3 years.
Population of deer is given by function,
[tex]P(t)=767(3^{\frac{t}{3} } )[/tex] , where t represent number of years.
For present population, substitute t = 0 in above function.
[tex]P(0)=767(3^{\frac{0}{3} } )=767[/tex]
Now, find When population become three times,
[tex]767(3^{\frac{t}{3} } )=767*3\\\\3^{\frac{t}{3} }=3^{1} \\\\\frac{t}{3} =1\\\\t=3 years[/tex]
So, tripling time is 3 years.
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