Final Answer:
The number of grains is increasing so the function will model exponential is:
1) growth
Step-by-step explanation:
Exponential growth occurs when a quantity increases at a rate proportional to its current value. In this context, the statement "The number of grains is increasing" suggests a scenario where the quantity (number of grains) is growing rapidly, following an exponential pattern.
Exponential growth is characterized by a constant percentage increase over equal intervals of time, resulting in a compounded effect. The function that models this kind of growth is generally expressed in the form \(f(x) = a \cdot (1 + r)^x\), where \(a\) is the initial amount, \(r\) is the growth rate, and \(x\) is time.
In simpler terms, as the number of grains increases, each new increment contributes not only to the total count but also to the subsequent rate of increase. This compounding effect distinguishes exponential growth from linear or quadratic patterns. Linear growth involves a constant rate of increase, while quadratic growth is characterized by a squared relationship between the input and output.
Exponential decay, on the other hand, would describe a scenario where the quantity decreases over time. In the given context, since the number of grains is consistently increasing, it aligns with the characteristics of exponential growth, making option 1) "growth" the appropriate choice.