Answer
a.) image attached
b.) 56,000/ year
c.) 42,000 per year
Work Step by Step
a.) image attached
b.) To find the average rate of increase of profit between 2012 to 2014, you must find the slope of the line that goes through the two points that corresponds to those years. the two points are (2012, 62) and (2014, 174). to find the slope the equation is slope = $\frac{y2 - y1}{x2 - x1}$
= $\frac{174 - 62}{2014 - 2012}$ = $\frac{112}{2}$ = 56
Our y values are 1000 s, so the final answer is 56000/year
c.) to estimate the rate at which the profits were changing in 2012
the slope of the tangent line is approximately the same slope as the secant line passing through the points that go through 2011 to 2013 . Lets use the points of 2011 and 2013 to find the slope at 2012.
The points are (2011, 27) and (2013, 111)
slope = $\frac{y2 - y1}{x2 - x1}$
= $\frac{111 - 27}{2013 - 2011}$ = $\frac{84}{2}$ = 42
therefore the profit were changing at the rate of $42,000 per year
