I need help with this question please

Question

For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.

Use the table below for Part A, Part B, and Part C. 

X Y

0	0
1	2
2	8
3	26
4	80

Part A: Emily states that the exponential equation to represent the table is y = 3^x, but Emily made a mistake. What did Emily do incorrectly?

Part B: Find the correct exponential equation to represent the values in the table. 

Part C: Show your work to support your answer.

Answer 1

general form of an exponential equation is y=ab^x + c

plug in some (x,y) points

(0,0) gives 0=ab^0 - c

0 =a(1) - c (anything to the zero power = 1)

c=-a

the correct exponential function is y=3^x - 1

y=ab^2 +c where a=1, b=3 and c=-a=-1

the tables shows points (0,0), (1,2), (2,8), (3,26) and (4,80)

plug them into y=3^x -1

0=3^0 -1 = 1-1 = 0

2=3^1-1 = 3-1 = 2

8=3^2-1= 9-1 = 8

26=3^3-1 = 27-1 = 26

80 =3^4-1 = 81-1=80

it works

Emily left out the c term, the constant term