Question

The graph of y=-3x+2 intersects the graph of an exponential function at (-1,5). Which of the following could be the

Answer 1

Answer:

$y=10(2)^{x}$

Step-by-step explanation:

Given:

The graph of $y=-3x+2$ intersects the exponential function at $(-1,5)$.

So, the point $(-1,5)$ must also lie on the exponential function.

Let us check each option for $y$ value at $x = -1$.

The option that gives $y= 5$ is the correct option.

Option 1:

$y=10(2)^{x}\\y=10(2)^{-1}\\y=10\times \frac{1}{2}=\frac{10}{2}=5$

Option 2:

$y=10(0.5)^{x}\\y=10(0.5)^{-1}\\y=10\times \frac{1}{0.5}=\frac{10}{0.5}=20$

Option 3:

$y=5^{x}\\y=5^{-1}\\y=\frac{1}{5}=0.2$

Option 4:

$y=5(2)^{x}\\y=5(2)^{-1}\\y=5\times \frac{1}{2}=\frac{5}{2}=2.5$

Therefore, only option 1 gives 5 for $y$ when $x=-1$

So, the correct option is $y=10(2)^{x}$