Question 193252
To Solve:  {{{1500=350e^(.02t)}}}

You must first isolate the e^x component -- so divide both sides by 350:

{{{ 1500 / 350 = e^(.02t) }}}

Simplifying gives you:

{{{ 30 / 7 = e^(.02t) }}}

Next, take the natural log (ln) of both sides:

{{{ ln(30/7) = ln(e^(.02t)) }}}

Now, use the power rule {{{ ln(x)^n = n * ln(x) }}} to simplify the right side:

{{{ ln(30/7) = .02t*ln(e) }}}

Since {{{ ln(e) = 1 }}}, you're left with:

{{{ ln(30/7) = .02t }}}

Divide both sides by .02 to get:

{{{ (ln(30/7)/.02) = t }}}

<font color="blue">So t = 72.76 years</font>
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Hope this helps.
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~ Joe