Find the equation of the exponential function represented by the table below: xx yy
0 4
1 16
2 64
3 256

  y = 4·4^x

Step-by-step explanation:

We can write the exponential function in the form ...

  y = a·b^x

The y-value for x=0 is 4, so that is the multiplier 'a' in our equation.

The ratio of values between x=1 and x=0 is 16/4 = 4, so that is the value of 'b' in the equation. The equation is ...

  y = 4·4^x

Additional comment

This could also be written ...

  y = 4^(x+1)

__

Consider the values for x=0 and x=1.

  x=0: y = a·b^0 = a

  x=1: y = a·b^1 = ab

Then the ratio of values is (ab)/(a) = b.

This is the fact that we used in the above working.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

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