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Bela started studying how the number of branches on her tree grows over time. Every 2.92.92, point, 9 years, the number of branches increases by an additional 83\%83%83, percent, and can be modeled by a function, NNN, which depends on the amount of time, ttt (in years). When Bela began the study, her tree had 606060 branches. Write a function that models the number of branches ttt years since Bela began studying her tree.

Respuesta :

Answer:

[tex]N(t)=60(1.83)^{t/2.9}[/tex]

Step-by-step explanation:

If an initial number of branches [tex]N_o[/tex] increases at a rate r% for a duration of t years in k periods, the Number of branches (N(t) at any time t will be modeled by the equation:

[tex]N(t)=N_{0}(1+r)^{t/k}[/tex]

Initially Bela's tree had 60 branches, therefore, [tex]N_o[/tex]=60.

Rate of Increase, r=83%=0.83

Period, k=2.9 Years

Therefore, the number of branches (after t years)

[tex]N(t)=60(1+0.83)^{t/2.9}\\N(t)=60(1.83)^{t/2.9}[/tex]

The function that models the number of branches t years since Bela began studying her tree is  [tex]N(t)=60(1.83)^{t/2.9}[/tex]

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