Question 60480
Good question. Great question. Let's go through it.
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So, we start of with the equation B=100e^kt, and the fact that B=5287 when t=13. With this in mind we can easily solve for k as shown below:
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{{{5287 = 100e^(13k)}}} (divide both sides by 100)
{{{52.87 = e^(13k)}}} (natural log of both sides, which cancels out the e)
{{{ln(52.87) = 13k}}} (divide both sides by 13)
{{{ln(52.87)/13 = k}}}
{{{k = 0.305}}} (to three significant figures)
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Hope all that helps.