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254 Chapter 3 Exponential and Logarithmic Functions<br />
32. (a)<br />
6000 33. (a)<br />
4 16<br />
1500<br />
(b)<br />
P <br />
110<br />
162.4<br />
1 0.34e 0.5609x<br />
(b)<br />
6000<br />
0 11<br />
0<br />
(c)<br />
4 16<br />
1500<br />
This model is a good fit.<br />
4827.2<br />
S 1018.4 <br />
1 e t8.13911.9372<br />
Using a graphing utility, t 15.7 or 2005.<br />
The model is a good fit.<br />
34. (a)<br />
2000<br />
3 14<br />
0<br />
(b) Linear model: y 18.5x 1365<br />
Quadratic model: 2.10x 2 54.2x 1230<br />
Cubic model: y 0.071x 3 0.30x 2 39.9x 1265<br />
Power model: y 1239.7 x 0.0985<br />
Exponential model: y 1370.41.012 x<br />
(c)<br />
Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003<br />
Linear 1439 1458 1476 1495 1513 1532 1550 1569 1587 1606<br />
Quadratic 1413 1449 1480 1507 1529 1548 1562 1572 1578 1580<br />
Cubic 1415 1448 1478 1505 1529 1548 1563 1573 1578 1577<br />
Power 1421 1453 1479 1502 1522 1539 1555 1570 1584 1596<br />
Exponential 1437 1455 1472 1490 1508 1526 1544 1563 1581 1600<br />
Answers will vary.<br />
(d) For 2015, x 25 and y 1273 million metric tons.<br />
35. (a) Linear model: y 15.71t 51.0<br />
Logarithmic model: y 134.67 ln t 97.5<br />
Quadratic model: y 1.292t 2 38.96t 45.0<br />
Exponential model: y 85.971.091 t<br />
Power model: y 37.27t 0.7506<br />
––CONTINUED––<br />
© Houghton Mifflin Company. All rights reserved.
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