65, 73, 78
Banking In Exercises 63-68, determine how long it takes to double the given investment if r is the interest are made. rate and the interest is compounded continuously. Assume that no withdrawals or further deposits 63. Initial Amount: $1,500; r = 6% 64. Initial Amount: $3,000; r = 4% 65. Initial Amount: $4,000; r = 5.75% 66. Initial Amount: $6,000; r = 6.25% 67. Initial Amount: $2,700; r = 7.5% Davon Of the lula fo 68. Initial Amount: $3,800; r = 5.8% Banking An initial deposit is made in a bank account. In Exercises 69-74, find the interest rate r if the interest is compounded continuously and no withdrawals or further deposits are made. 69. Initial Amount: $1,500; Amount in 5 years: $2,000 70. Initial Amount: $3,000; Amount in 3 years: $3,600 71. Initial Amount: $4,000; Amount in 8 years: $6,000 72. Initial Amount: $6,000; Amount in 10 years: $12,000 73. Initial Amount: $8,500; Amount in 5 years: $10,000 74. Initial Amount: $12,000; Amount in 20 years: $25,000 75. Bacterial Growth Suppose a colony of bacteria doubles in 12 hours from an initial population o 1 million. Find the growth constant k if the population is modeled by the function Poek. When will the population reach 4 million? 8 million? 76. Bacterial Growth Suppose a colony of bacteria doubles in 20 hours from an initial population 1 million. Find the growth constant k if the population is modeled by the function Poek. Whe will the population reach 4 million? 8 million? cop77. Computer Science In 1965, Gordon Moore, then director of Intel research, conjectured that th Jarfi pollon number of transistors that fit on a computer chip doubles every few years. This came to b known as Moore's Law. Analysis of data from Intel Corporation yields the following model A noiron the number of transistors per chip over time: or s(t) = 2297.10.3316ti where s( t) is the number of transistors per chip, and t is the number of years since 1971. (Source: Intel Corporation Hi got a. What is the number of transistors per chip in 1971 according to this model? b. How long does it take to double the number of transistors? 78. Depreciation The value of a 2003 Toyota Corolla is given by the function v(t) = 14000(0.93) where t is the number of years since its purchase and v(t) is its value in dollars. (Source: Kelley Blue Bo a. What was its initial purchase price? b. What percentage of its value does the Toyota Corolla lose each year? c. How long will it take for the value of the Toyota Corolla to reach $12,000
