The rainfall R(t) (in mm ) over the course of a year in Bali, Indonesia as a function of time t (in days) can be modeled by a sinusoidal expression of the form a*sin(b*t)+d. At t=0, in mid-April, the expected daily rainfall is 2.3mm, which is the average value throughout the year. One-quarter of the year later, at t=91.25, the rainfall is at its minimum, at an expected daily value of 1.4mm. Find R(t). t should be in radians. R(t)=◻

Question

The rainfall  R(t) (in  mm ) over the course of a year in Bali, Indonesia as a function of time  t (in days) can be modeled by a sinusoidal expression of the form  a*sin(b*t)+d. At  t=0, in mid-April, the expected daily rainfall is  2.3mm, which is the average value throughout the year. One-quarter of the year later, at  t=91.25, the rainfall is at its minimum, at an expected daily value of  1.4mm. Find  R(t).  t should be in radians.  R(t)=◻

Bytelearn · Accepted Answer

Identify average rainfall value: Identify the average rainfall value d, which is the midline of the sinusoidal function. d = 2.3 mmDetermine amplitude of function: Determine the amplitude a of the sinusoidal function, which is the difference between the average and minimum rainfall values. a = 2.3 mm - 1.4 mm a = 0.9 mmCalculate value of b: Calculate the value of b, which is related to the period of the sinusoidal function. Since the minimum occurs at t=91.25 days, and this represents one-quarter of the year, the period is 4 times 91.25 days. Period = 4 * 91.25 days Period = 365 days Since the period T is related to b by the formula T = (2π)/b, we can solve for b. b = 2π / 365Write equation for R(t): Write the equation for R(t) using the values of a, b, and d. R(t) = a*sin(b*t) + d R(t) = 0.9*sin((2π/365)*t) + 2.3

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