- #1

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- 6

## Homework Statement

In my book, there is a formula that gives the amount (in grams) of Radium in a jar after t years (100 grams were initially stored):

R = 100⋅e

^{-0.00043⋅t}

The book asks me to sketch the graph of the equation. I decided to find a point where the time elapsed equals the remaining radium to use as a point for the sketch. This is were I found a problem.

## Homework Equations

The properties of logarithms are relevant.

## The Attempt at a Solution

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The equation is:

R = 100⋅e

^{-0.00043⋅t}

I am looking for the point in time where t = R. I substitute:

t = 100⋅e

^{-0.00043⋅t}

Then I divide by e

^{-0.00043⋅t}on both sides:

t/e

^{-0.00043⋅t}= 100

Take the natural log of both sides:

ln (t/e

^{-0.00043⋅t}) = ln (100)

Quotient property:

ln(t) - ln (e

^{-0.00043⋅t}) = ln(100)

ln (t) + 0.00043⋅t = ln (100)

Here is where I hit a block. I have t inside the logarithm. To get rid of the logarithm, I have raise e to both sides of the equation. If I do that, I make the t outside the logarithm an exponent while the other one isn't. I can't seem to find a way to bring the both "t"s together so that I can solve. Please help. Thanks. If I'm not clear somewhere please tell me.