Trigonometry Examples

Solve for t 140=(165-70)e^(-0.046(t))+70
Step 1
Rewrite the equation as .
Step 2
Subtract from .
Step 3
Move all terms not containing to the right side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Subtract from .
Step 4
Divide each term in by and simplify.
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Step 4.1
Divide each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Divide by .
Step 4.3
Simplify the right side.
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Step 4.3.1
Cancel the common factor of and .
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Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Cancel the common factors.
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Step 4.3.1.2.1
Factor out of .
Step 4.3.1.2.2
Cancel the common factor.
Step 4.3.1.2.3
Rewrite the expression.
Step 5
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 6
Expand the left side.
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Step 6.1
Expand by moving outside the logarithm.
Step 6.2
The natural logarithm of is .
Step 6.3
Multiply by .
Step 7
Divide each term in by and simplify.
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Step 7.1
Divide each term in by .
Step 7.2
Simplify the left side.
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Step 7.2.1
Cancel the common factor of .
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Step 7.2.1.1
Cancel the common factor.
Step 7.2.1.2
Divide by .
Step 7.3
Simplify the right side.
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Step 7.3.1
Move the negative in front of the fraction.
Step 7.3.2
Replace with an approximation.
Step 7.3.3
Divide by .
Step 7.3.4
Log base of is approximately .
Step 7.3.5
Divide by .
Step 7.3.6
Multiply by .