A spring bounces up and down according to the model d(t)=4sin(30t)+3 where d(t) is the displacement in cm from the rest position and t is time in seconds. What is the range?

The range of d(t) is [-1, 7]

Step-by-step explanation:

The range of d(t) can be found with the lowest and the highest value of the function.

The highest value of d(t) occurs when the sine function is equal to 1 (because the value multiplying the sine is a positive value), and the lowest function occurs when it is equal to -1.

So we have that:

d_max = 4*1 + 3 = 7

d_min = 4*(-1) + 3 = -1

So the range of d(t) is [-1, 7].

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