Question

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.

Answer 1

`N(t)=60(1.83)^(t/2.9)`

Explanation:

If an initial number of branches
`N_o` 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:

`N(t)=N_(0)(1+r)^(t/k)`

Initially Bela's tree had 60 branches, therefore,
`N_o`=60.

Rate of Increase, r=83%=0.83

Period, k=2.9 Years

Therefore, the number of branches (after t years)

`N(t)=60(1+0.83)^(t/2.9)\\N(t)=60(1.83)^(t/2.9)`

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