To determine the type of function that best models the data in the table, let's analyze the values:
- As \( x \) increases from 1 to 4, the values of \( y \) increase dramatically:
- \( y(1) = 10 \)
- \( y(2) = 100 \)
- \( y(3) = 1000 \)
- \( y(4) = 10000 \)
Examining the pattern:
- \( 10 \) (for \( x = 1 \)) is \( 10^1 \)
- \( 100 \) (for \( x = 2 \)) is \( 10^2 \)
- \( 1000 \) (for \( x = 3 \)) is \( 10^3 \)
- \( 10000 \) (for \( x = 4 \)) is \( 10^4 \)
This suggests an exponential growth factor where \( y = 10^x \).
Therefore, the type of function that best models the data is Exponential.
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