Step-by-step explanation:
step 1. what is the question? probably solve for x. okay.
step 2. 4^(2x) + 1 = 4
step 3. 4^(2x) = 3 subtract 1 from each side
step 4. ln4^(2x) = ln3 take on of each side
step 5. 2xln4 = ln3 definition of logs
step 6. 2x = ln3/ln4 divide both sides by ln4
step 7. x = ln3/2ln2^2 divide both side by 2 and replace 4 with 2^2
step 8. x = ln3/4ln2.
Answer:
(a) 3
Step-by-step explanation:
Calculate the slope m of the line given using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0,3) and (x₂, y₂ ) = (3, 2)
m = 
= - 
given a line with slope m then the slope of a line perpendicular to it is
= - 
= - 
= 3 → (a)
We can solve this by using the formula:
(x, y) (x + a, y + b) = (5,-4) (-2,1)
So, plugging in the values and solving for a and b,
5 + a = -2
a = -8
-4 + b = 1
b = 5
Therefore, the translation is
(x,y) (x - 8, y +5)
So, let's find the rates:
5 years = 1180 people
5n = 1180
n = 236
236*2 = 472
5600 + 472 = 6072
6072 people
