College Algebra, 2013a

490 Exponential and Logarithmic Functions
6.5.4 Answers
) 12t
1. ˆ A(t) = 500 ( 1+ 0.0075
12
ˆ A(5) ≈ $519.10, A(10) ≈ $538.93, A(30) ≈ $626.12, A(35) ≈ $650.03
ˆ It will take approximately 92 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 3.88. This means that the investment is growing at an average rate
of $3.88 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 4.85. This means that
the investment is growing at an average rate of $4.85 per year at this point.
2. ˆ A(t) = 500e 0.0075t
ˆ A(5) ≈ $519.11, A(10) ≈ $538.94, A(30) ≈ $626.16, A(35) ≈ $650.09
ˆ It will take approximately 92 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 3.88. This means that the investment is growing at an average rate
of $3.88 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 4.86. This means that
the investment is growing at an average rate of $4.86 per year at this point.
) 12t
3. ˆ A(t) = 1000 ( 1+ 0.0125
12
ˆ A(5) ≈ $1064.46, A(10) ≈ $1133.07, A(30) ≈ $1454.71, A(35) ≈ $1548.48
ˆ It will take approximately 55 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 13.22. This means that the investment is growing at an average rate
of $13.22 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 19.23. This means that
the investment is growing at an average rate of $19.23 per year at this point.
4. ˆ A(t) = 1000e 0.0125t
ˆ A(5) ≈ $1064.49, A(10) ≈ $1133.15, A(30) ≈ $1454.99, A(35) ≈ $1548.83
ˆ It will take approximately 55 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 13.22. This means that the investment is growing at an average rate
of $13.22 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 19.24. This means that
the investment is growing at an average rate of $19.24 per year at this point.
) 12t
5. ˆ A(t) = 5000 ( 1+ 0.02125
12
ˆ A(5) ≈ $5559.98, A(10) ≈ $6182.67, A(30) ≈ $9453.40, A(35) ≈ $10512.13
ˆ It will take approximately 33 years for the investment to double.