For this case, the first thing we should do is use the following equation:
f (x) = 200 (1.03) ^ x
We substitute f (x) = 300:
300 = 200 (1.03) ^ x
We clear the value of x:
log1.03 (300/200) = log1.03 ((1.03) ^ x)
x = log1.03 (300/200)
x = 13.72
Answer:
the population will first reach 300 in about 13.72 years.
Answer:
10) - 45 degrees
12) 0 degrees
Step-by-step explanation:
10)
Find the x and y components that define the vector that joins C with D:
x-component: -4 - (-8) = - 4 + 8 = 4
y-component: 4 - 8 = -4
use the tangent function to find the angle
:

12)
Find the x and y components that define the vector that joins A with B:
x-component: 7 - 4 = 3
y-component: - 1 - (-1) = -1 + 1 = 0
use the tangent function to find the angle
:

Answer:

Step-by-step explanation:
The general form of a quadratic polynomial is given by:
(1)
You have the following polynomial:
(2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
(3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):

Then, the factorization of the polynomial is:
