Anyone good with quadratics out there?
The total resources T (in billions of dollars), the government agency that insures pensions can be approximated by the equation T = -0.26x^2 + 3.62x + 30.18, where is x is the number of years after 2000. Determine when the total resources are at the given level, a: $27 billion, b: $30 billion and c: when will the government be out of money (T = 0).

Question

Anyone good with quadratics out there?
The total resources T (in billions of dollars), the government agency that insures pensions can be approximated by the equation T = -0.26x^2 + 3.62x + 30.18, where is x is the number of years after 2000.  Determine when the total resources are at the given level, a: $27 billion, b: $30 billion and c: when will the government be out of money (T = 0).

dape · Answer

You can invert the equation with the quadratic formula and throw away the negative solution, we then get
$$ x ≈ 6.96154 + 0.0384615\sqrt{111229-2600T} $$
Now just plug in the different T's.

anonymous · Answer

I'm not coming up with anything that makes sense.

dape · Answer

For example for T=0:
$$ x ≈ 6.96154+0.0384615\sqrt{111229-2600*0} ≈ 19.7889 \,\, years$$

anonymous · Answer

thank you!  i am doing the math right after all.  thanks for the confirmation.