Question

1. which of the following equations is best represented by the table below?

x	0	1	2	3	4
y	3	7	27	127	627

options:

• $y = 5^x + 11$
• $y = 5^x$
• $y = 5^x - 4$
• $y = 5^x + 2$

Explanation:

Step1: Test $x=0$ in options

For $x=0$, $5^0=1$.

• $y=5^0+11=12

eq 3$

• $y=5^0=1

eq 3$

• $y=5^0-4=-3

eq 3$

• $y=5^0+2=3$, matches $y=3$

Step2: Test $x=1$ in valid option

For $x=1$, $5^1=5$.
$y=5^1+2=7$, matches $y=7$

Step3: Test $x=2$ in valid option

For $x=2$, $5^2=25$.
$y=25+2=27$, matches $y=27$

Step4: Test $x=3$ in valid option

For $x=3$, $5^3=125$.
$y=125+2=127$, matches $y=127$

Step5: Test $x=4$ in valid option

For $x=4$, $5^4=625$.
$y=625+2=627$, matches $y=627$

Answer:

$\boldsymbol{y=5^x - 2}$