Lenmana started studying how the number of branches on her tree grows over time. The number of branches
increases by a factor of every 3.5 years, and can be modeled by a function, N, which depends on the
amount of time, t (in years).
When Lenmana began the study, her tree had 48 branches
Write a function that models the number of branches t years since Lenmana began studying her tree.

Solution:

Given that,

The number of branches  increases by a factor of every 3.5 years

Let the function be N

t is the amount of time in years

When Lenmana began the study, her tree had 48 branches

The increasing function is given as:

Where,

N is the function ( future value )

a is the initial value

b is the growth factor

t is number of years

From given,

a = 48

b = 3.5

Therefore,

Thus the function that models the number of branches t years since Lenmana began studying her tree is found