342 STEP 4. Review the Knowledge You Need to Score High
Therefore,P=200
(
1
99)
e.^369 t1 +(
1
99)
e.^369 t=
200 e.^369 t
99 +e.^369 t=
200
99 e−.^369 t+ 1. On day 10,
P=200
99 e−.369(10)+ 1=
200
3. 472
≈ 57 .600, sowe would predict that approximately 58
students would be infected on the tenth
day.- Applyyn=yn− 1 +Δx· f′(xn− 1 ,yn− 1 ) with
Δx= 0 .1. (See table below.) - Applyyn=yn− 1 +Δx· f′(xn− 1 ,yn− 1 ) with
Δx= 0 .5. (See table below.)
Solution to Problem 24.
x y dy/dx Nexty-value
01 − 10. 9
0.1 0.9 − 0. 719 0. 8281
0.2 0.8281 − 0. 52787 0. 775313075
0.3 0.775313 − 0. 37605 0. 737708202
0.4 0.737708 − 0. 24147 0. 713561134
0.5 0.713561y(5)≈0.713561Solution to Problem 25.
x y dy/dx Calculate nexty-value
01 1 1 + 0 .5(1)
0.5 1.5 .5 1. 5 + 0 .5(0.5)
1 1.75 − 0. 25 1. 75 + 0 .5(− 0 .25)
1.5 1.625 − 1. 375 1. 625 + 0 .5(− 1 .375)
2 0.9375 − 3. 0625 0. 9375 + 0 .5(− 3 .0625)
2.5 − 0. 59375 − 5. 59375 − 0. 59375 + 0 .5(− 5 .59375)
3 − 3. 390625y(3)≈− 3. 391