Question

3) People who use computers at their job are listed in the table by ages. Age group Age used to represent group (years) Percent 18-25 21.5 344 25-29 27 48.3 30-39 34.5 50.7 40 - 49 44.5 513 50 - 59 545 Over 59 625 27 a Let Pit) be the percentage of workers who use computers at age t years. Use the regression capabilities of your calculator to find the quadratic equation. Use the middle column for b. Use P to estimate the percentage of 23 year old workers who use computers on the job.

Answer 1

a) quadratic equation for P(t) is

P(t)= -0.051167 t2 + 4.08862 t-28.13953

b) when age is 23 , t=23 . apply t=23 and find P(t) to get this

P(23)=-0.051167 *232 + 4.08862*23-28.13953 = 38.831387

on rounding this it becomes 38.83

so 38.83 % of age 23 uses computer

c) this is a quadratic equation of the form f(x) =ax2+bx+c.

maximum of this function occur when a is negative and and occurs at

$\LARGE x= \frac{-b}{2a}$

to find maximum find function value at this point.

for our function a= -0.051167 ,b=4.08862 . so maximum occur at

t = -4.08862 2 * -0.051167 39.95368 39.95

so age group at 39.95 uses maximum computer. it can be round to 40 . so age 40 uses maximum computer

find P(39.95) to get maximum percentage

P(39.95)=-0.051167 *39.952 + 4.08862*39.95-28.13953 = 53.53817

on rounding it becomes 53.54

so maximum percentage is 53.54

d) when halfe of workers use computer ,P(t) becomes 50 . apply P(t)=50 and solve

50=-0.051167 *t2 + 4.08862t-28.13953

on rearrainging

-0.051167 *t2 + 4.08862t- 78.13953=0

this is a quadratic equation of the form ax2+bx+c=0 .

solution for this is given by following quadratic formula

T = -67762 - 4ac 2a

here a= -0.051167 ,b=4.08862 , c=-78.13953

apply to equation and find t

or   

so for age 31.6 and 48.3 exactely 50% uses computer .

on rounding this becomes 48 and 32 ages