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Page 64 - 9 To solve for k divide both sides by 6.7e 9...

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Huynh, Kazyak, Rees, Ufner Page 64, #2 A newspaper article from The New York Times on May 27,1990 is given to us, but there are three blanks we need to fill in. First blank compounded daily at 6%. Because the interest is compounded at a continuous rate, we use the equation P(t) = P o e kt where P o is the initial value at t=0, k is the rate the interest is being compounded (in percent), and t is the amount of time (in years) since t=0. P(t) = P o e kt P(t) = 450,000e (.06)(213) = $1.6e 11 Second blank compounded annually. The interest is now compounded once a year, so we use the equation P(t) = P o a t P(t) = P o a t P(t) = 450,000(1.06) 213 = $1.1e 11 Third blank interest compounded by second. Because seconds are continuous, we use the P(t) = P o e kt equation. This time, we want to solve for k, by substituting in what we know for P o , t, and P(t). P(t) = P o e kt 1.6e 11 = 450,000e (k)(6.7e 9 ) We divide both sides by 450,000. 355,555 = e (k)(6.7e 9 ) To eliminate e and bring the exponent down, take ln of both sides. ln(355,555) = k(6.7e
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Unformatted text preview: 9 ) To solve for k, divide both sides by 6.7e 9. $1.9e-9 = k 213 Years After Loan, Uncle Sam is Dunned by Lisa Belkin SAN ANTONIO, May 26 – More than 200 years ago, a wealthy Pennsylvania merchant named Jacob DeHaven lent $450,000 to the Continental Congress to rescue the troops at Valley Forge. That loan was apparently never repaid. So Mr. DeHaven’s descendants are taking the United States Government to court to collect what they believe they are owed. The total: $1.6e 11 in today’s dollars if the interest is compounded daily at 6 percent, the going rate at the time. If compounded yearly, the bill is only $1.6e 11 . FAMILY IS FLEXIBLE The descendants say that they are willing to be flexible about the amount of a settlement and that they might even accept a heartfelt thank you or perhaps a DeHaven statue. But they also note that interest is accumulating at $1.9e-9 a second....
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