Answer:
C. 4.5 inches
Step-by-step explanation:
Given the following data;
Force, F = 10 pounds
Extension, e = 3 inches
First of all, we would determine the spring constant (k) using the following formula;
Force = spring constant * extension
10 = spring constant * 3
Spring constant = 10/3
Spring constant = 3.33 pounds per inches.
Next, we would find the extension of the spring when a force of 15 pounds is applied;
F = ke
15 = 3.33 * e
Extension, e = 15/3.33
Extension, e = 4.5 inches.
This is the graph of 1/x moved 4 units to the left
so its f(x) = 1 / (x + 4)
C
The number of cows is given by
So, after 
years, the number of cows will be
We want this number to be twice as much as the original:
First of all, we can cancel 14 from both sides:
Finally, on the right hand side, we can use the exponent rule
to get
To solve this equation, we must impose that the two exponents are the same:
And clearly this is true if and only if 
. So, it will take 5 years for the cow heard to double in number.
You can do the exact same steps to find the doubling time for the sheeps.
[-3,1)
-x-6<_-3 add 6 both sides
-x<_3 divide by negative 1 which means sign switches
x>_-3
-4x+3>-1 subtract 3 both sides
-4x>-4 divide by negative 4 which means sign switches
x<1
1 is the greater bound meaning x can’t be larger than 1
the sign doesn’t include 1 so it’s the parenthesis in interval notation
-3 is the lower bound meaning x can’t be -3 or less than -3 so the interval notation is
The sign includes -3 so it’s brackets in interval notation
