Page 176 - How To Solve Word Problems In Calculus

To find k we use the given information u(3) = 40.

40 = 20 + 50e 3k

20 = 50e 3k

2
e 3k =
5
2
3k = ln
5

1 2
k = ln
3 5
The general solution becomes

2
1
( ln )t
u(t) = 20 + 50e 3 5
= 20 + 50(e ln 2 5 ) t/3

t/3
2
= 20 + 50
5
To find the temperature after 6 minutes, we compute u(6).

2
2
u(6) = 20 + 50
5

4
= 20 + 50
25
= 28

The temperature after 6 minutes is 28 Fahrenheit.
◦
Supplementary Problems

1. The growth rate of a bacteria culture is proportional to the number
of bacteria present. If a population whose size is initially 100
bacteria doubles every 2 hours,

163