Nyala is bungee jumping. The following function gives her elevation, in meters, t seconds after jumping:...

Question

Nyala is bungee jumping. The following function gives her elevation, in meters, t seconds after jumping:
E(t) = \frac{80 \sin(0.6t)}{t} + 15
What is the instantaneous rate of change of Nyala's elevation after 5 seconds?
Choose 1 answer:
A) 9.96 meters per second
B) -9.96 seconds per meter
C) 17.26 meters per second
D) 17.26 seconds per meter

SnapAndSolve AI · Accepted Answer

To find the instantaneous rate of change of Nyala's elevation after 5 seconds, we need to find the derivative of E(t) and evaluate it at t = 5.

The function is E(t) = \frac{80 \sin(0.6t)}{t} + 15.

Using the quotient rule for differentiation, the derivative E'(t) is:

E'(t) = \frac{d}{dt} \left( \frac{80 \sin(0.6t)}{t} \right) = \frac{t \cdot (80 \cdot 0.6 \cos(0.6t)) - 80 \sin(0.6t)}{t^2}.

Evaluating this at t = 5:

E'(5) = \frac{5 \cdot (80 \cdot 0.6 \cos(3)) - 80 \sin(3)}{25}.

Calculating this gives approximately -9.96 meters per second.

The correct answer is A) 9.96 meters per second.

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Nyala is bungee jumping. The following function gives her elevation, in meters, t seconds after jumping:...

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