Solve for t 5/10=(10(1-e^(-0.2t)))/10

Math
510=10(1-e-0.2t)10
Rewrite the equation as 10(1-e-0.2t)10=510.
10(1-e-0.2t)10=510
Factor each term.
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Reduce the expression by cancelling the common factors.
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Reduce the expression 10(1-e-0.2t)10 by cancelling the common factors.
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Cancel the common factor.
10(1-e-0.2t)10=510
Rewrite the expression.
1-e-0.2t1=510
1-e-0.2t1=510
Divide 1-e-0.2t by 1.
1-e-0.2t=510
1-e-0.2t=510
Cancel the common factor of 5 and 10.
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Factor 5 out of 5.
1-e-0.2t=5(1)10
Cancel the common factors.
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Factor 5 out of 10.
1-e-0.2t=5⋅15⋅2
Cancel the common factor.
1-e-0.2t=5⋅15⋅2
Rewrite the expression.
1-e-0.2t=12
1-e-0.2t=12
1-e-0.2t=12
1-e-0.2t=12
Move all terms not containing t to the right side of the equation.
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Subtract 1 from both sides of the equation.
-e-0.2t=12-1
To write -1 as a fraction with a common denominator, multiply by 22.
-e-0.2t=12-1⋅22
Combine -1 and 22.
-e-0.2t=12+-1⋅22
Combine the numerators over the common denominator.
-e-0.2t=1-1⋅22
Simplify the numerator.
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Multiply -1 by 2.
-e-0.2t=1-22
Subtract 2 from 1.
-e-0.2t=-12
-e-0.2t=-12
Move the negative in front of the fraction.
-e-0.2t=-12
-e-0.2t=-12
Multiply each term in -e-0.2t=-12 by -1
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Multiply each term in -e-0.2t=-12 by -1.
(-e-0.2t)⋅-1=-12⋅-1
Multiply (-e-0.2t)⋅-1.
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Multiply -1 by -1.
1e-0.2t=-12⋅-1
Multiply e-0.2t by 1.
e-0.2t=-12⋅-1
e-0.2t=-12⋅-1
Multiply -12⋅-1.
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Multiply -1 by -1.
e-0.2t=1(12)
Multiply 12 by 1.
e-0.2t=12
e-0.2t=12
e-0.2t=12
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(e-0.2t)=ln(12)
Expand the left side.
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Expand ln(e-0.2t) by moving -0.2t outside the logarithm.
-0.2tln(e)=ln(12)
The natural logarithm of e is 1.
-0.2t⋅1=ln(12)
Multiply -0.2 by 1.
-0.2t=ln(12)
-0.2t=ln(12)
Divide each term by -0.2 and simplify.
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Divide each term in -0.2t=ln(12) by -0.2.
-0.2t-0.2=ln(12)-0.2
Cancel the common factor of -0.2.
t=ln(12)-0.2
Simplify ln(12)-0.2.
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Move the negative in front of the fraction.
t=-ln(12)0.2
Divide 1 by 2.
t=-ln(0.5)0.2
Rewrite.
t=–0.693147180.2
Divide -0.69314718 by 0.2.
t=–3.4657359
Multiply -1 by -3.4657359.
t=3.4657359
t=3.4657359
t=3.4657359
Solve for t 5/10=(10(1-e^(-0.2t)))/10

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