Question

choose the function that is graphed below.
choose 1 answer:
a ( y = 5 cdot 5^x )
b ( y = 10^x )
c ( y = 5 cdot 2^x )

Explanation:

Step1: Test x=0 on all functions

For option A: $y=5 \cdot 5^0 = 5 \cdot 1 = 5$
For option B: $y=10^0 = 1$
For option C: $y=5 \cdot 2^0 = 5 \cdot 1 = 5$
The graph passes through $(0,5)$, so eliminate option B.

Step2: Test x=1 on remaining functions

For option A: $y=5 \cdot 5^1 = 5 \cdot 5 = 25$
For option C: $y=5 \cdot 2^1 = 5 \cdot 2 = 10$
The graph passes through $(1,10)$, so eliminate option A.

Step3: Verify with x=2

For option C: $y=5 \cdot 2^2 = 5 \cdot 4 = 20$
The graph shows the value at $x=2$ is 20, which matches.

Answer:

C. $y = 5 \cdot 2^x$