Question

Howard started studying how the number of branches on his tree grows over time.
The relationship between the elapsed time t, in years since Howard started studying the tree, and the
number of its branches, N(t), is modeled by the following function: N(t)=38 x (9/5) ^ t/7.3

Answer 1

Answer:

howards tree gains 4/5 more branches every 7.3 years

Step-by-step explanation:

took one for the team

Answer 2

The time when the tree gains 4/5 more branches is every 2.92 years approx 3 years

What is a Function ?

A function is a Mathematical statement used to relate a dependent and an independent variable.

The function represents relationship between the elapsed time t, in years since Howard started studying the tree, and the number of its branches, N(t)

$\rm N(t)= 38 * (\dfrac {9}{5})^{\dfrac{t}{7.3}$

When the branch will have 4/5 more branches if initially it has 38 branches

Time when branches = 38 +(4/5) = 38.8

38.8  = 38  * $\rm (\dfrac {9}{5})^{\dfrac{t}{7.3}$

1.02 =  $\rm (\dfrac {9}{5})^{\dfrac{t}{7.3}$

$\rm 1.8^{0.4} = {1.8}^{t/7.3}$

on equating ,

0.4 = t / 7.3

t = 2.92 years.

Therefore , The time when the tree gains 4/5 more branches is every 2.92 years approx 3 years

The complete question is Howard's tree gains  4/5 more branches every ___ years.

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