Question

x | y
0 | 500
1 | 600
2 | 720
3 | 864
4 | 1,036.8
5 | 1,244.16
which equation describes the relationship shown in the table?
a. $y = 1.2(500)^x$
b. $y = 500 + 100x$
c. $y = 500(1.2)^x$
d. $y = 100 + 500x$
a
b
c
d

Explanation:

Step1: Analyze Option A

For \( x = 0 \), \( y = 1.2(500)^0 = 1.2\times1 = 1.2
eq 500 \). So A is wrong.

Step2: Analyze Option B

For \( x = 2 \), \( y = 500 + 100\times2 = 700
eq 720 \). So B is wrong.

Step3: Analyze Option C

For \( x = 0 \), \( y = 500(1.2)^0 = 500\times1 = 500 \). For \( x = 1 \), \( y = 500(1.2)^1 = 600 \). For \( x = 2 \), \( y = 500(1.2)^2 = 720 \). It matches the table values.

Step4: Analyze Option D

For \( x = 1 \), \( y = 100 + 500\times1 = 600 \), but for \( x = 2 \), \( y = 100 + 500\times2 = 1100
eq 720 \). So D is wrong.

Answer:

C. \( y = 500(1.2)^x \)