Question

Statistics show that the fractional part of a battery, B, that is still good after t hours of use is given by B=5^−0.01t. What fractional part of the battery is still operating after 400 hours of use?

Answer 1

Answer: 1/625

Given:

$B=5^{-0.01t}$

To find what fractional part of the batter is still operating after 400 hours of use, we just need to substitute t = 400 to the given equation.

$B=5^{-0.01t}$$B=5^{-0.01(400)}$$B=0.0016\text{ or }\frac{1}{625}$

Therefore, a fractional part of 0.0016 of 1/625 of the batter is still operating after 400 hours of use.