`1000e^(-4x) = 75` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 30 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Divide both sides by 1000

`e^(-4x)=3/40 `

Take the ln of both sides and bring down the exponent

`-4xlne=ln(3/40) `

Simplify,

`x=0.648 `

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loves2learn | (Level 3) Salutatorian

Posted on

To solve equations, you need to isolate the variable.

Divide both sides by 1000 (you need to do the same thing on both sides)

`e^(-4x)=4/30 `

Use a ln because you can use its' properties to bring down the x so you can solve for it.

Given,

`a^x=b `

Then

`lna^x=lnb `

and `xlna=lnb `

Therefore,

`lne^(-4x)=ln(3/40) `

`-4xlne=ln(3/40) `

`lne=1 ` , so simplifies to,

`-4x=ln(3/40) `

Divide both sides by -4 and simplify,

`x=0.648 `

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