To determine whether a linear or exponential model best fits the given data, we need to examine the rate of change in costs as the number of lemons increases.
Looking at the costs provided:
- From 1 to 3 lemons: Cost increases from $0.89 to $2.67 (difference of $1.78)
- From 3 to 5 lemons: Cost increases from $2.67 to $4.45 (difference of $1.78)
- From 5 to 9 lemons: Cost increases from $4.45 to $8.01 (difference of $3.56)
- From 9 to 12 lemons: Cost increases from $8.01 to $10.68 (difference of $2.67)
The differences are not consistent, indicating that the cost does not increase by a constant rate. Instead, it appears that the increments become larger as the quantity of lemons increases.
Since the rate of change is not constant (the increase in cost is not the same for each additional lemon), this suggests that the cost does not follow a linear function. Instead, it is indicative of varying percentage increases, which would be characteristic of an exponential function.
Therefore, the best model for the increase in the cost of lemons is:
An exponential function, because the rate of increase is a constant percent rate of change.
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