Q:

PLEASE HELP WITH THESE 2 QUESTIONS!!!1.What is the linear function equation represented by the graph?2.Function f is an exponential function. It predicts the value of a famous sculpture, in thousands of dollars, as a function of the number of years since it was last purchased.What equation models this function?

Accepted Solution

A:
Answer:[tex]y=-\frac{1}{2}x + 1[/tex][tex]y=5(\frac{7}{5})^x[/tex]Step-by-step explanation:(1)Lets pick two points from the first graph (0,1)  and (2,0)The graph is linear so we use equation y=mx+bwhere m is the slope and b is the y intercepty intercept at (0,1)  so y intercept b = 1now we find slope m using formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] [tex]m=\frac{0-1}{2-0}=\frac{-1}(2}[/tex]m=-1/2  and b=1  so equation y=mx+b becomes[tex]y=-\frac{1}{2}x + 1[/tex](2) Pick two point from graph (0,5) (1,7)Since it is an exponential graph, we use y=ab^xfor (0,5) the equation becomes [tex]5=ab^0 so a=5[/tex] for (1,7) the equation becomes [tex]7=ab^1[/tex]We know a= 5, so [tex]7=5b^1[/tex][tex]b=\frac{7}{5}[/tex]The equation y=ab^x becomes[tex]y=5(\frac{7}{5})^x[/tex]