Question

the table list data regarding the average salaries of professional athletes in the years 1991 and 2001

1991 262,000
2001 1,390,000

a: use the data points to find a linear function that fits the data
b:use the function to predict the average salary in 2005 and 2010

S(x)=?

Answer 1

if we set 1991 as year 0
and set 2001 as year 10
we get
S(0) = 262 000
S(10) = 1 390 000
for a linear function we have
S(x) = a * x + b
for the first it is easy to see
S(0) = a * 0 + b = 262 000
b = 262 000
and the second gives
S(10) = a * 10 + 262 000 = 1 390 000
a * 10 = 1 390 000 - 262 000 =>
a * 10 = 1 128 000
a = 112 800
S(x) = 112 800 * x + 262 000
then insert for x = 14 for year 2005
S(14) = 112 800 * 14 + 262 000
S(14) = 1 841 200
and x = 19 for year 2010
S(19) = 112 800 * 19 + 262 000
S(19) = 2 405 200