Lenmana started studying how the number of branches on her tree grows over time. The number of branches increases by a factor of
11/6 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.
The formula for <u>exponential growth</u>is y = ab^x.
To write this equation, we know it has to start with 48 (which is the variable a). We need to add the rate of growth. This is 11/6 (which is variable b). But we also need to account for the "every 3.5 years" part, so divide the x as an exponent by 3.5.
N(t) = 48 * 11/6^(t/3.5)
This equation is easy to test, and it's a good idea to test it after you write it. For example, after 3.5 years we know that it should have 48*11/6 branches. Does our equation work? Yes.
