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

Reduce the expression by cancelling the common factors.

Reduce the expression 10(1-e-0.2t)10 by cancelling the common factors.

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.

Factor 5 out of 5.

1-e-0.2t=5(1)10

Cancel the common factors.

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

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.

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.

(-e-0.2t)⋅-1=-12⋅-1

Multiply (-e-0.2t)⋅-1.

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.

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 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 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.

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