Use the graph to answer the question. What is equation shown in the graph? (1 point)

Question

image shows a graph with axes x from -5 to 5 and y from 10 down to 0. Points are -2, 1.28 and 1, 2.5

Responses y=2⋅−(1.25)x y is equal to 2 times negative 1 point 2 5 to the x th power y=2⋅(1.25)x y is equal to 2 times 1 point 2 5 to the x th power y=1.25⋅(2)x y is equal to 1 point 2 5 times 2 to the x th power y=−2⋅(1.25)x

Answer 1

To determine the correct equation from the given options based on the provided points (-2, 1.28) and (1, 2.5), we can analyze the points in relation to the equations.

1. Exponential Growth/Decay: The options provided suggest that the graph might be an exponential function of the form \( y = a \cdot b^x \), where \( a \) and \( b \) are constants.

2. Checking the given points:

   • For the point (-2, 1.28):
   • Substitute \( x = -2 \) into the equations and check if \( y \) approximates to 1.28.
   • For the point (1, 2.5):
   • Substitute \( x = 1 \) into the equations and check if \( y \) approximates to 2.5.

3. By testing each option with the points:

• For Option 1: \( y = 2 \cdot (-1.25)^x \)

  • At \( x = -2 \): \( y = 2 \cdot (-1.25)^{-2} \) (Not applicable since we cannot take negative base to a power)

• For Option 2: \( y = 2 \cdot (1.25)^x \)

  • At \( x = -2 \): \( y = 2 \cdot (1.25)^{-2} \approx 2 \cdot 0.64 \approx 1.28 \) (Valid)
  • At \( x = 1 \): \( y = 2 \cdot (1.25)^1 = 2 \cdot 1.25 = 2.5 \) (Valid)

• For Option 3: \( y = 1.25 \cdot (2)^x \)

  • At \( x = -2 \): \( y = 1.25 \cdot (2)^{-2} = 1.25 \cdot 0.25 = 0.3125 \) (Not valid)

• For Option 4: \( y = -2 \cdot (1.25)^x \)

  • At \( x = -2 \): \( y = -2 \cdot (1.25)^{-2} < 0 \) (Not valid)

Based on the calculations, Option 2:

\( y = 2 \cdot (1.25)^x \)

is the only option that satisfies both points.

Therefore, the answer is: y = 2 \cdot (1.25)^x.

Answer 2

now another image with x axis from -10 to 10 and 15 down to 0 with points 0, 10 and 1,10.5

Answer 3

Given the new points (0, 10) and (1, 10.5) and the information about the axes, we can analyze potential equations to see which one matches the behavior of these points.

Analysis of the Points:

1. Point (0, 10):

   • This means that when \( x = 0 \), \( y = 10 \). For an exponential function of the form \( y = a \cdot b^x \), this would imply \( a = 10 \) when \( x = 0 \) (since any number raised to the power of 0 is 1).

2. Point (1, 10.5):

   • This means that when \( x = 1 \), \( y = 10.5 \). This suggests that the \( b \) value shouldn't be too far from 1, as the output increases slightly from 10 to 10.5.

Possible Forms of the Equation:

The general form of an exponential equation we might look for is:

• \( y = a \cdot b^x \), where \( a \) is the value at \( x = 0 \) (which is 10) and \( b \) is the growth factor.

So we can initially write:

• \( y = 10 \cdot b^x \)

From point (1, 10.5):

• Setting up the equation for this point gives us:
  • \( 10 \cdot b^1 = 10.5 \)
  • \( b = \frac{10.5}{10} = 1.05 \)

Proposed Equation:

Based on these calculations, the equation that fits these points could be:

• \( y = 10 \cdot (1.05)^x \)

Conclusion:

If there are specific options to choose from, you can compare this derived formula to the choices given. If not, based on the points described, the equation for the graph highlighted by these points would be:

\( y = 10 \cdot (1.05)^x \).