Question

The x-axis ranges from 0 to 10 in increments of 2. The y-axis
ranges from 0 to 35,000 in increments of 5,000. The curve
begins at the point left parenthesis 0 comma 30,000 right
parenthesis and passes through the points left parenthesis 1
comma 22,500 right parenthesis, left parenthesis 2 comma
16,875 right parenthesis, left parenthesis 3 comma 12,656.25
right parenthesis, left parenthesis 4 comma 9492.19 right
parenthesis, left parenthesis 5 comma 7119.14 right
parenthesis, left parenthesis 6 comma 5339.36 right
parenthesis, left parenthesis 7 comma 4004.52 right
parenthesis, left parenthesis 8 comma 3003.39 right
parenthesis, and left parenthesis 9 comma 2252.54 right
parenthesis. The curve continues with an arrowhead on the
end.

Given the graph of the exponential equation representing the
value of a car since purchase, which option is the correct
exponential equation for the graph if the graph goes through the
points and ?
(1 point)
(0, 30000) (1, 22500)
y = 0.75(30, 000)
x
y = 22, 500( )
3
4
x
y = 30, 000( )
3
4
x
y = 30, 000( )
4
3
x

Answer 1

y = 30,000(3/4)^x

Reason: y(0) = 30000 gives the initial value 30000. The decay factor = y(1)/y(0) = 22500/30000 = 3/4, so the model is 30000*(3/4)^x.