Linear function

Question

An employee's salary during certain years is given in the table below. Suppose s(t) is the employee's salary, where t is the number of years since 2010

Year 2010 2013 2016 2019

Salary in dollars 37,600 39,400 41,200 43,000

a. Does the function S(t) appear to be a linear function? Explain how you know including calculations.

b. Find the slope of the function S(t). Include the units of this slope.

C. Find a formula for S(t).

D Using your formula for S(t), what would you expect the employee's salary to be in 2025?

Answer 1

a. Does the function S(t) appear to be a linear function? Explain how you know including calculations. Yes, this function is linear. The x values are all increasing by 3, the y values are all increasing by 1800. Increasing at a constant rate means it must be linear.

b. Find the slope of the function S(t). Include the units of this slope. Slope is rise/run. We already have these values from part a, increasing by 1800 every 3 years. 1800/3 = 600

C. Find a formula for S(t). The formula for a linear equation is S(t)=mt+b We already have the slope, b is the y intercept, the initial value when x=0 would be the year 2010. b=37600 So the equation is:

S(t)=600t+37600

D Using your formula for S(t), what would you expect the employee's salary to be in 2025? t is the number of years since 2010. So t=15. plug this into the equation.

S(25)=600(15)+37600 = 46,600