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

Type of Function

x y
1
1
10
10
2
2
100
100
3
3
1000
1000
4
4
10000
10000


(1 point)
Responses

linear
linear

exponential
exponential

cubic
cubic

quadratic

1 answer

To determine which type of function best models the data in the table, let's analyze the values provided:

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

Looking closely at these \( y \) values, we can see a pattern where the \( y \) value increases significantly as \( x \) increases. In particular, the \( y \) values appear to be powers of 10:

  • For \( x = 1 \), \( y = 10^0 = 1 \)
  • For \( x = 2 \), \( y = 10^2 = 100 \)
  • For \( x = 3 \), \( y = 10^3 = 1000 \)
  • For \( x = 4 \), \( y = 10^4 = 10000 \)

This suggests that the relationship follows an exponential function, specifically \( y = 10^{x} \).

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