Question

13. The average retail prescription price of drugs in dollars from 2002 to 2004 is described in the following table as y. Price, y, in dollars Y ear 2002 55.37 2003 59.52 2004 63.59 Use a system of equations to find the equation of the parabola y = at2 + bt+c that passes through the points. Let t 2 correspond to 2002. Solve the system and write the equation of the parabola that passes through these points. 19, what is the least amount of money that must be invested for 10 years at 5% annual interest rate with interest compounded continuously in order for the investment to grovw to at least $22,000?

Answer 1

13. The average retail prescription price of drugs in dollars from 2002 to 2004 is described in the following table as y Price, y, in dollars Year 2002 55.37 2003 59.52 2004 63.59 Use a system of equations to find the equation of the parabola y- at +bt+c that passes through the points. Let 2 corespond to 2002. Solve the system and write the equation of the parabola that passes through these points Ans.: v-at +bt C (2,55.37)4a+ 2b+c 55.37 (3,59.52)9a+3b+c 59.52 4,63.59) 16a +4b+c63.59 Subtract 4a +2b+c 55.37 from9a +3b+c 59.52, this gives, 9a +3b +c-4a- 2b-c- 59.52 55.37 5a +b-4.1510a+2b 8.30 Subtract 4a +2b+c 55.37 from 16a+4b+c 63.59, this gives 16a 4b c 4a-2b-c 63.59- 55.37 12a +2b 8.22

By solving 10a +2b 8.30 and 12a 2b 8.22, this gives, 5a+b 4.15b 4.15-5a 4.15 0.2 4.35 4a+ 2b + c 55.37→ c = 46.83 -0 04° + 4.3 5t + 46.83 Equation of the parabola : y 19, What is the least amount of money that must be invested for 10 years at 5% annual interest rate with interest compounded continuously in order for the investment to grow to at least $22,000? Ans.: Let A-S22.000,-0.05. t-10 years, P-? 22000 Pe°05*10 22000 : $13,344