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Miriam is studying the growth rate of bacteria. She puts the data in the following table, where x represents minutes and y represents the number of bacteria.

x

0

1

2

3

y

0.08

0.4

2

10

Which type of function is represented by the data in the table?

(1 point)
Responses

exponential growth
exponential growth

exponential decay
exponential decay

linear
linear

quadratic
quadratic

1 answer

To determine the type of function represented by the data in the table, we can analyze the growth of the number of bacteria (y) over time (x).

The data provided is:

  • At \( x = 0 \), \( y = 0.08 \)
  • At \( x = 1 \), \( y = 0.4 \)
  • At \( x = 2 \), \( y = 2 \)
  • At \( x = 3 \), \( y = 10 \)

Looking at the values of \( y \):

  • From \( 0.08 \) to \( 0.4 \) (a factor increase of 5).
  • From \( 0.4 \) to \( 2 \) (a factor increase of 5).
  • From \( 2 \) to \( 10 \) (a factor increase of 5).

The increases are not constant (i.e., they're not equal, which would indicate linear growth), but they seem to increase by a factor of 5 each time, which suggests that the relationship may be exponential.

Based on this analysis, the type of function represented by the data in the table is:

exponential growth.