Question

Aleksandra started studying how the number of branches on her tree grows over time. Every 1.51.51, point, 5 years, the number of branches increases by an addition of \dfrac{2}{7} 7 2 ​ start fraction, 2, divided by, 7, end fraction of the total number of branches. The number of branches can be modeled by a function, NNN, which depends on the amount of time, ttt (in years). When Aleksandra began the study, her tree had 525252 branches. Write a function that models the number of branches ttt years since Aleksandra began studying her tree. N(t) =N(t)=N, left parenthesis, t, right parenthesis, equals

Answer 1

52(9/7)^t/1.5

Explanation:

The function N(t) a which models the number of branches t years after Aleksandra began studying her trees ;

Initial number of branches = 52

Increment every 1.5 years = 2/7

N(t) = Initial * (1 + r)^t

t expressed per year = t/1.5

Hence,

N(t) = 52(1 + 2/7)^t/1.5

N(t) = 52(9/7)^t/1.5