Finite Math Examples

Solve for t 200/(1+8e^(-0.3t))=100
Step 1
Multiply both sides by .
Step 2
Simplify.
Tap for more steps...
Step 2.1
Simplify the left side.
Tap for more steps...
Step 2.1.1
Cancel the common factor of .
Tap for more steps...
Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.2
Simplify the right side.
Tap for more steps...
Step 2.2.1
Simplify .
Tap for more steps...
Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Multiply.
Tap for more steps...
Step 2.2.1.2.1
Multiply by .
Step 2.2.1.2.2
Multiply by .
Step 3
Solve for .
Tap for more steps...
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Divide each term in by and simplify.
Tap for more steps...
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Tap for more steps...
Step 3.3.3.1
Cancel the common factor of and .
Tap for more steps...
Step 3.3.3.1.1
Factor out of .
Step 3.3.3.1.2
Cancel the common factors.
Tap for more steps...
Step 3.3.3.1.2.1
Factor out of .
Step 3.3.3.1.2.2
Cancel the common factor.
Step 3.3.3.1.2.3
Rewrite the expression.
Step 3.4
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3.5
Expand the left side.
Tap for more steps...
Step 3.5.1
Expand by moving outside the logarithm.
Step 3.5.2
The natural logarithm of is .
Step 3.5.3
Multiply by .
Step 3.6
Divide each term in by and simplify.
Tap for more steps...
Step 3.6.1
Divide each term in by .
Step 3.6.2
Simplify the left side.
Tap for more steps...
Step 3.6.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.6.2.1.1
Cancel the common factor.
Step 3.6.2.1.2
Divide by .
Step 3.6.3
Simplify the right side.
Tap for more steps...
Step 3.6.3.1
Move the negative in front of the fraction.
Step 3.6.3.2
Replace with an approximation.
Step 3.6.3.3
Divide by .
Step 3.6.3.4
Log base of is approximately .
Step 3.6.3.5
Divide by .
Step 3.6.3.6
Multiply by .