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Which type of function best models the data in the table?

Type of Function

x y
1
10
2
100
3
1000
4
10000


(1 point)
Responses

linear
linear

quadratic
quadratic

exponential
exponential

cubic

1 answer

To determine the best model for the given data points:

  • When \( x = 1, y = 10^1 = 10 \)
  • When \( x = 2, y = 10^2 = 100 \)
  • When \( x = 3, y = 10^3 = 1000 \)
  • When \( x = 4, y = 10^4 = 10000 \)

From this pattern, we see that as \( x \) increases, \( y \) is proportional to \( 10 \) raised to the power of \( x \). This indicates an exponential relationship.

Therefore, the type of function that best models the data in the table is exponential.