Question

Astronomers have observed that sunspots very sinusoidally the variations from a minimum of about 10 sunspots per year to a maximum of about 120 per year cycle lasts about 11 years of Eminem occurred in 1964 which function can model the number of sunspots SS a function of the year T let me see.

A. S(t) = 55sin(π(t - 1964) / 11) + 65
B. S(t) = 65sin(π(t - 1964) / 11) + 55
C. S(t) = -55cos(2π(t - 1964) / 11) + 65

Answer 1

The best mathematical model for the number of sunspots as a function of time is S(t) = 55sin(\(\pi(t - 1964) / 11\)) + 65, taking into account the 11-year average sunspot cycle and the minimum that occurred in 1964.

Step-by-step explanation:

The correct function to model the number of sunspots as a function of the year is: S(t) = 55sin(\(\pi(t - 1964) / 11\)) + 65. This sinusoidal function accurately represents the cyclic nature of the sunspot average cycle, with an amplitude of 55, which accounts for the fluctuation between a minimum of about 10 sunspots and a maximum of about 120 sunspots.

The function has an offset of 65 to adjust the baseline to the midrange of the sunspot counts. The cycle period of about 11 years is taken into account by dividing the inside of the sine function by 11. This allows the function to complete one full cycle as time changes by 11 years. Moreover, the time 't' is adjusted by subtracting 1964, the year when a minimum occurred, to align the sinusoidal cycle with historical data.