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244 Chapter 3 Exponential and Logarithmic Functions
22.
1
2 C Cek24,100
1
2 e24,100k
23.
y ae bx 24.
1 ae b0 ⇒ 1 a
10 e b3
y ae bx
1
2 aeb0 ⇒ a 1 2
k ln12
24,100
0.4 Ce ln1224,1001000
C0.97165
C 0.41 g
ln 10 3b
ln 10
3
b ⇒ b 0.7675
Thus, y e 0.7675x .
5 1 2 eb4
10 e 4b
ln 10 4b
b
ln 10
4
0.5756
Thus, y 1 2 e0.5756x .
25.
0, 4 ⇒ a 4 26.
5, 1 ⇒ 1 4e b5 ⇒ b 1 5 ln 1 4
1 ln 4 0.2773
5
y 4e 0.2773x
1
ln 4 3b
ln14
3
y ae bx
1 ae b0 ⇒ 1 a
1
4 eb3
b ⇒ b 0.4621
Thus, y e 0.4621x .
27. (a) Australia: 0, 19.2, 10, 20.9
a 19.2 and 20.9 19.2e b10 ⇒ b 0.008484
y 19.2e 0.008484t
For 2030, y 24.8 million.
Canada: 0, 31.3, 10, 34.3
a 31.3 and 34.3 31.3e b10 ⇒ b 0.009153
y 31.3e 0.009153t
For 2030, y 41.2 million.
Philippines: 0, 79.7, 10, 95.9
a 79.7 and 95.9 79.7e b10 ⇒ b 0.0185
y 79.7e 0.0185t
For 2030, y 138.8 million.
South Africa: 0, 44.1, 10, 43.3
a 44.1 and 43.3 44.1e b10 ⇒ b 0.00183
y 44.1e 0.00183t
For 2030, y 41.7 million.
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