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

Answer:

$N(t)=60(1.83)^{t/2.9}$

Step-by-step 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  $N(t)=60(1.83)^{t/2.9}$