Solved on Dec 16, 2023

After 100 hours, the fractional part of the battery $B$ still operating is $5^{-0.01 \cdot 100} = 0.368$ .

STEP 1

Assumptions
1. The fractional part of a battery that is still good after $t$ hours is given by $B=5^{-0.01t}$ .
2. We want to find the fractional part of the battery still operating after $t=100$ hours.

STEP 2

To find the fractional part of the battery still operating after 100 hours, we substitute $t=100$ into the given formula.
$B=5^{-0.01t}$

STEP 3

Now, plug in $t=100$ into the equation.
$B=5^{-0.01 \times 100}$

STEP 4

Simplify the exponent by multiplying $-0.01$ by $100$ .
$B=5^{-1}$

STEP 5

Calculate the value of $5^{-1}$ .
$B=5^{-1} = \frac{1}{5}$

STEP 6

Convert the fraction to a decimal if necessary.
$B=\frac{1}{5} = 0.2$
The fractional part of the battery that is still operating after 100 hours of use is $0.2$ .

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After 100 hours, the fractional part of the battery $B$ still operating is $5^{-0.01 \cdot 100} = 0.368$ .

STEP 1

Assumptions
1. The fractional part of a battery that is still good after $t$ hours is given by $B=5^{-0.01t}$ .
2. We want to find the fractional part of the battery still operating after $t=100$ hours.

STEP 2

To find the fractional part of the battery still operating after 100 hours, we substitute $t=100$ into the given formula.
$B=5^{-0.01t}$

STEP 3

Now, plug in $t=100$ into the equation.
$B=5^{-0.01 \times 100}$

STEP 4

Simplify the exponent by multiplying $-0.01$ by $100$ .
$B=5^{-1}$

STEP 5

Calculate the value of $5^{-1}$ .
$B=5^{-1} = \frac{1}{5}$

STEP 6

Convert the fraction to a decimal if necessary.
$B=\frac{1}{5} = 0.2$
The fractional part of the battery that is still operating after 100 hours of use is $0.2$ .

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After 100 hours, the fractional part of the battery BBB still operating is 5−0.01⋅100=0.3685^{-0.01 \cdot 100} = 0.3685−0.01⋅100=0.368.

STEP 1

Assumptions1. The fractional part of a battery that is still good after ttt hours is given by B=5−0.01tB=5^{-0.01t}B=5−0.01t.2. We want to find the fractional part of the battery still operating after t=100t=100t=100 hours.

STEP 2

To find the fractional part of the battery still operating after 100 hours, we substitute t=100t=100t=100 into the given formula.B=5−0.01tB=5^{-0.01t}B=5−0.01t

STEP 3

Now, plug in t=100t=100t=100 into the equation.B=5−0.01×100B=5^{-0.01 \times 100}B=5−0.01×100

STEP 4

Simplify the exponent by multiplying −0.01-0.01−0.01 by 100100100.B=5−1B=5^{-1}B=5−1

STEP 5

Calculate the value of 5−15^{-1}5−1.B=5−1=15B=5^{-1} = \frac{1}{5}B=5−1=51​

STEP 6

Convert the fraction to a decimal if necessary.B=15=0.2B=\frac{1}{5} = 0.2B=51​=0.2The fractional part of the battery that is still operating after 100 hours of use is 0.20.20.2.

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After 100 hours, the fractional part of the battery $B$ still operating is $5^{-0.01 \cdot 100} = 0.368$ .

Assumptions
1. The fractional part of a battery that is still good after $t$ hours is given by $B=5^{-0.01t}$ .
2. We want to find the fractional part of the battery still operating after $t=100$ hours.

To find the fractional part of the battery still operating after 100 hours, we substitute $t=100$ into the given formula.
$B=5^{-0.01t}$

Now, plug in $t=100$ into the equation.
$B=5^{-0.01 \times 100}$

Simplify the exponent by multiplying $-0.01$ by $100$ .
$B=5^{-1}$

Calculate the value of $5^{-1}$ .
$B=5^{-1} = \frac{1}{5}$

Convert the fraction to a decimal if necessary.
$B=\frac{1}{5} = 0.2$
The fractional part of the battery that is still operating after 100 hours of use is $0.2$ .