Rate at which risk of down syndrome is changing is approximated by function r (x) = 0.004641x2 - 0.3012x + 4.9 (20 ≤ x ≤ 45) where r (x) measured in percentage of births per year and x is maternal age at delivery. find function f giving risk as percentage of births when maternal age at delivery is x years, given that risk of down syndrome at 30 is 0.14% of births.

The rate of change of the risk of down syndrome (in percentage of births per year) is

r (x) = 0.004641x² - 0.3012x + 4.9, 20≤ x ≤ 45

where

x = maternal age at delivery.

The function giving risk as a percentage of births when maternal age is x is the integral of r (x). That is,

f (x) = 0.001547x³ - 0.1506x² + 4.9x + c

When x = 30, f = 0.14%. Therefore

0.001547 (30³) - 0.1506 (30²) + 4.9 (30) + c = 0.14

41.769 - 135.54 + 147 + c = 0.14

c = - 53.089

Answer:

f (x) = 0.001547x³ - 0.1506x² + 4.9x - 53.089, 20 ≤ x ≤ 45

The function is graphed as shown below.