Jason earned gross wages of $887.12. His deductions were: $69 in federal withholding taxes, 6.2% in social security taxes, 1.45% in Medicare taxes, $82.95 in health insurance, and $25 in union dues. Find Jason’s net pay.

(a) Profit equation
Profit = revenue - cost
unit profit = revenue per unit - cost per unit = 16-7.3=8.7
profit
p(x) = (unit profit)*x=8.7x

(b) profit over time
sales,
x(t) = 1000 * (100 * (ln(t^2+87)+48.8)
=100000 ln(t^2+0.87)+48800

profit,
P(t)
=p(x(t))-5200000
=p(100000 ln(t^2+0.87)+48800)-5200000
=8.7(100000 ln(t^2+0.87)+48800)-5200000
=870000*ln((t^2+0.87))-4775440

(c)
Break even quantity is when p(x)-5200000=0, 
solving,
8.7x-5200000=0 =>
x=5200000/8.7
=597701.1
=597702 (rounded to next integer)

(d)
Time t to reach break even is when
P(t)=0
or
solve for t in 
870000*ln((t^2+0.87))-4775440=0
ln(t^2+0.87)=4775440/870000=5.489
raise powers to base of e
t^2+0.87=e^(5.489)=242.018
t=sqrt(242.018-0.87)=15.53 months.