The slope equals $0.10 (since $1.00 per 10 tokens translates to $0.10 per token)
The y-intercept is $60 (the fixed yearly membership fee)
The linear equation is y = 0.10x + 60 (following y = mx + b)
The domain consists of all x values where x ≥ 0 (negative token quantities are impossible)
The range includes all y values with y ≥ 60 (plugging the domain values into the function)
The y-intercept of this function stands at $60
The correct option is C) $197,263.70. It has decreased 6% annually over the last three years.
The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.
The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.
Thus, the total rate of salt flow, represented by 
in grams, is defined by the differential equation,
which is linear. Shift the 
term to the right side, then multiply both sides by 
:
Next, integrate both sides and solve for :
Initially, the tank contains 5 g of salt at time 
, so we have
The duration required for the tank to contain 20 g of salt is 
, such that
By solving the equation -x+8+3x=x-6, we rearrange it to 2x+8=x-6. This leads to the simplification 2x-x=-6-8, yielding x=-14. The correct answer is letter B.
