The cumulative number (in thousands).... Please Help!!!

Question

The cumulative number (in thousands) of deaths from a certain disease from 200 to 2010 may be modeled by A= 2.39x^2+5.04x+5.1, where x=0 corresponds to 2000, x=1 to 2001,etc.Use the formula for A to estimate symbolically the year when the total number of deaths reached 110 thousand.

Answer 1

Method 1:  Put the formula into Excel and get:

    x     Cumulative deaths (*1000)

    0       5.100
    1      12.520
    2      24.700
    3      41.640
    4      63.340
    5      89.800
    6     121.020
    7     157.000
    8     197.740
    9     243.240
  10     293.500

 

O.K., method 2:  Solve a quadratic formula:

    2.39x^2 + 5.04x + 5.1 = 110

    239x^2 + 504x - 10490 = 0          (*100, I have trouble with decimals)

                       (put a, b, c into quadratic formula to solve for x)

     x = 5.654    or    x = -7.763        (but, we know x cannot be negative)

 

Just past mid-year 2005 (x=5), the cumulative number (in thousands) of deaths will pass 110.  So, as we verified this using Excel.