Question

which exponential equation contains the points $(-1,5)$ and $(2,5000)$? (1 point)
$\bigcirc\\ y = 50\cdot(10)^{x}$
$\bigcirc\\ y = -50\cdot(10)^{x}$
$\bigcirc\\ y = 50\cdot-(10)^{x}$
$\bigcirc\\ y = (500)^{x}$

Explanation:

Step1: Test point $(-1,5)$ in Option A

Substitute $x=-1$: $y = 50 \cdot (10)^{-1} = 50 \cdot \frac{1}{10} = 5$

Step2: Test point $(2,5000)$ in Option A

Substitute $x=2$: $y = 50 \cdot (10)^2 = 50 \cdot 100 = 5000$

Step3: Verify other options fail

Option B: $x=-1$ gives $y=-5$, not 5.
Option C: $x=-1$ gives $y=-5$, not 5.
Option D: $x=-1$ gives $y=\frac{1}{500}$, not 5.

Answer:

A. $y = 50 \cdot (10)^x$