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.

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

Step-by-step 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)

no this is a nonlinear negative

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°