Question

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?

Answer 1

`y=-(1)/(2)x + 1`

`y=5((7)/(5))^x`

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+b

where m is the slope and b is the y intercept

y intercept at (0,1) so y intercept b = 1

now we find slope m using formula
`(y_2-y_1)/(x_2-x_1)`

`m=(0-1)/(2-0)=\frac{-1}(2}`

m=-1/2 and b=1 so equation y=mx+b becomes

`y=-(1)/(2)x + 1`

(2) Pick two point from graph (0,5) (1,7)

Since it is an exponential graph, we use y=ab^x

for (0,5) the equation becomes
`5=ab^0 so a=5`

for (1,7) the equation becomes
`7=ab^1`

We know a= 5, so
`7=5b^1`

`b=(7)/(5)`

The equation y=ab^x becomes

`y=5((7)/(5))^x`