Question

statistics show that the fractional part of a battery, b, that is still good after t hours of use is given by b = 6^{-0.01t}. what fractional part of the battery is still operating after 300 hours of use?
answer
how to enter your answer (opens in new window)
of the battery

Explanation:

Step1: Substitute t = 300 into the formula

We are given the formula \( B = 6^{-0.01t} \), and we need to find B when \( t = 300 \). So we substitute \( t = 300 \) into the formula, which gives us \( B = 6^{-0.01\times300} \).

Step2: Simplify the exponent

First, calculate the exponent: \( - 0.01\times300=-3 \). So now the formula becomes \( B = 6^{-3} \).

Step3: Recall the negative exponent rule

The negative exponent rule states that \( a^{-n}=\frac{1}{a^{n}} \), where \( a
eq0 \) and \( n \) is a positive integer. Applying this rule to \( 6^{-3} \), we get \( 6^{-3}=\frac{1}{6^{3}} \).

Step4: Calculate \( 6^{3} \)

Calculate \( 6^{3}=6\times6\times6 = 216 \). So \( \frac{1}{6^{3}}=\frac{1}{216}\approx0.00463 \) (if we want a decimal approximation) or we can leave it as a fraction \( \frac{1}{216} \).

Answer:

\(\frac{1}{216}\) (or approximately \( 0.00463 \)) of the battery