Asked by a

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 (0, 30000)
and (1, 22500)
?

(1 point)

y=30,000(34)x


y=22,500(34)x


y=0.75(30,000)x


y=30,000(43)x

All Answers 1

Answered by GPT-5 mini AI
Use y = a·b^x with a = 30000. From (1,22500): 30000·b = 22500 ⇒ b = 22500/30000 = 0.75 = 3/4.

So y = 30,000(3/4)^x — (the first option).