Final answer:
In a simple linear decrease, as N (interpreted as frequency) increases, λ (wavelength) decreases due to the inverse relationship between frequency and wavelength. However, if the question is referring to a decay constant in radioactive decay, λ is constant.
Step-by-step explanation:
When considering the relationship between wavelength (λ) and the number of occurrences or cycles (N) in a simple linear decrease, it's important to understand that if one has a fixed length of a cycle and the number of cycles increases, then the wavelength must decrease. This relationship is based on the inverse correlation between frequency and wavelength. Specifically, in a simple linear decrease which might refer to a scenario where there's a direct, inversely proportional relationship between the two quantities, as the number of cycles or events (N) increases, the wavelength (λ) decreases.
The decay constant (λ) in the context of radioactive decay as given by the formula N = Noe-t, where e is the base of natural logarithms, represents a different concept than the wavelength mentioned earlier. Here, the decay constant (λ) is related to the rate at which a substance undergoes radioactive decay and is not directly related to changes in wavelength or frequency in the electromagnetic spectrum.
In electromagnetic theory, according to the universal wave equation, the product of the frequency (f) and the wavelength (λ) of light equals a constant (the speed of light), so if the frequency increases, the wavelength decreases. Therefore, without more context, if we assume the question refers to wave frequency and its linear relationship with wavelength, as N (interpreted as frequency) increases in a simple linear decrease, λ (wavelength) decreases. However, if the question is referring to a decay constant in a radioactive decay scenario where N represents the number of remaining nuclei, λ would be the decay constant, which remains unchanged during the decay process.