Answer:
The answer to the equation is: 4.648
Answer:
there are no extraneous solutions to the equation
Step-by-step explanation:
Given
= x + 2 ( square both sides )
8x + 9 = (x + 2)² ← expand
8x + 9 = x² + 4x + 4 ( subtract 8x + 9 from both sides )
0 = x² - 4x - 5 ← in standard form
0 = (x - 5)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 5 : 
= 
= 7
right side = 5 + 2 = 7
left side = right side ⇒ x = 5 is a solution
x = - 1 : 
= 
= 1
right side = - 1 + 2 = 1
left side = right side ⇒ x = - 1 is a solution
There are no extraneous solutions
If the population decreases by 2% each year, that can be represented by multiplying the population by 0.98 mathematically. So if it decreases by 2% each year, an equation we can use is:
P*(0.98)^t,
where P is the current population and t is the number of years.
So in 2020, that would be 10 years from now, so the population would be:
1759*(0.98)^10 = 1437.23
Or about 1437 people.
How long till it is less than 1000? We can set up an inequality and solve:
1759*(0.98)^t < 1000
(0.98)^t < 1000/1759
t*ln(0.98) < ln(1000/1759)
t > ln(1000/1759)/(ln(0.98)) (swap the sign because ln(0.98) is a negative #)
t > 27.95
So the population would be below 1000 in about 28 years, or 2038.
Answer:
$22,071.39
Step-by-step explanation:
= 500*[(1-0.77928606825)/.005]
= 500*44.14278635
= $22,071.39
