College Algebra, 2013a

6.5 Applications of Exponential and Logarithmic Functions 491
ˆ The average rate of change from the end of the fourth year to the end of the fifth year
is approximately 116.80. This means that the investment is growing at an average rate
of $116.80 per year at this point. The average rate of change from the end of the thirtyfourth
year to the end of the thirty-fifth year is approximately 220.83. This means that
the investment is growing at an average rate of $220.83 per year at this point.
6. ˆ A(t) = 5000e 0.02125t
ˆ A(5) ≈ $5560.50, A(10) ≈ $6183.83, A(30) ≈ $9458.73, A(35) ≈ $10519.05
ˆ It will take approximately 33 years for the investment to double.
ˆ The average rate of change from the end of the fourth year to the end of the fifth year
is approximately 116.91. This means that the investment is growing at an average rate
of $116.91 per year at this point. The average rate of change from the end of the thirtyfourth
year to the end of the thirty-fifth year is approximately 221.17. This means that
the investment is growing at an average rate of $221.17 per year at this point.
8. P = 2000 ≈ $1985.06
e 0.0025·3 5000
9. P = ≈ $3993.42
(1+ 0.0225
12 ) 12·10
10. (a) A(8) = 2000 ( 1+ 0.0025 ) 12·8
12 ≈ $2040.40
ln(2)
(b) t =
12 ln ( 1+ 0.0025 ) ≈ 277.29 years
12
(c) P =
2000
(
1+
0.0025
12
) 36
≈ $1985.06
11. (a) A(8) = 2000 ( 1+ 0.0225 ) 12·8
12 ≈ $2394.03
ln(2)
(b) t =
12 ln ( 1+ 0.0225 ) ≈ 30.83 years
12
2000
(c) P = ( )
1+
0.0225 36
≈ $1869.57
12
(d) ( 1+ 0.0225 ) 12
12 ≈ 1.0227 so the APY is 2.27%
12. A(3) = 5000e 0.299·3 ≈ $12, 226.18, A(6) = 5000e 0.299·6 ≈ $30, 067.29
15. ˆ k = ln(1/2)
14. ˆ k = ln(1/2)
5.27
≈−0.1315
ˆ t = ln(0.1)
−0.1315 ≈ 17.51 years.
ˆ A(t) =50e −0.1315t
14
≈−0.0495
ˆ A(t) =2e −0.0495t
ˆ t = ln(0.1)
−0.0495
≈ 46.52 days.