Question

Aleksandra started studying how the number of branches in her tree grows over time. Every 1.5 years, the number of branches increases by an addition of 2/7 of the total number of branches. The number of branches be modeled by a function, N, which depends on the amount of time, t (in years).

when aleksandra began the study, her tree had 52 branches.

Write a function that models the number of branches t years since aleksandra began studying her tree.

Answer 1

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

Explanation:

This problem can be modelated as an exponencial problem, using the formula:

N = Po * (1+r)^(t/1.5)

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

In our case, we have that N is the final number of branches after t years, Po = 52 branches, r = 2/7 and t is the number of years since the beginning (in the formula we divide by 1.5 because the rate is defined for 1.5 years)

Then, we have that:

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

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