6
advanced-math

The charge of an EV battery decreases by 4% for every hour of use. Which expression represents the charge remaining after hh hours, starting from 100%?

A

100(0.04)h100(0.04)^h

B

100(1.04)h100(1.04)^h

C

100(0.96)h100(0.96)^h

D

100(4)h100(4)^h

Correct Answer: C

Choice C is the correct answer. Decay rate rr converts to decay factor b=1rb = 1 - r.

  1. Identify Rate: The rate of decrease is r=4%=0.04r = 4\% = 0.04.
  2. Calculate Factor: For decay, b=1r=10.04=0.96b = 1 - r = 1 - 0.04 = 0.96.
  3. Form Equation: The initial value is 100, so y=100(0.96)hy = 100(0.96)^h.

💡 Strategic Tip: "Decreasing by r%r\%" means you keep (100r)%(100-r)\% of the value.

Choice A is incorrect because 0.04 would mean losing 96% per hour. Choice B is incorrect because 1.04 represents growth, not decay. Choice D is incorrect because 4 represents a 300% increase.