Section 1.6 Homework

2. This is similar to Section 1.6 Problem 24: For the equation 50e^(0.01t)=30, solve for t using natural logarithms. Use a decimal. Keep 2 decimal places (rounded at the last step). Answer: t= _____

-160.94 🔑 -160.94

3. This is similar to Section 1.6 Problem 42: Simplify the natural logarithm ln (4e)^(−8)+8ln 4. Answer: _____

-8 🔑 -8

5. This is Section 1.6 Problem 48: If Lucy deposits $3,000 into an account that pays interest at an annual rate of 6% compounded continuously, it takes ____ years for the investment to reach $5,500.

10.07 🔑 10.1

4. This is similar to Section 1.6 Problem 46: If Joe deposits $7500 into an account that pays interest at an annual rate of 4.5% compounded continuously, it takes (keep 2 decimals) ____ years for the investment to reach $12000.

10.44 🔑 10.44

7. This is Section 1.6 Problem 52: It takes ____ years for an investment, at an annual interest rate of 3.8%, compounded continuously, to double its value.

18 🔑 18.24

1. This is Section 1.6 Problem 16: For the equation e^t=20, solve for t using natural logarithms. Use a decimal. Keep 3 decimal places (rounded at the last step). Answer: t= ____

2.996 🔑 2.996

9. This is Section 1.6 Problem 64: A business associate who owes Ana $4,000 offered to pay her $3,800 now or to pay her $2,000 now and $2,000 two years later. Using only financial reasons to make her decision, and assume that the interest is compounded continuously, she should switch choices at the annual interest rate _____ %.

5.3 🔑 5.3

6. This is similar Section 1.6 Problem 50: The Lopez family has $18000 to invest. What should the annual interest rate be, compounded continuously, in order for the investment to grow to $32000 in 6 years? Answer: The annual interest rate should be (keep 2 decimal places) ____ %.

9.59 🔑 9.59

8. This is Section 1.6 Problem 58: John deposits $8,000 into an account that pays interest at an annual rate of 5.1%, compounded continuously. (a) Find an expression for the amount in the account after t years. Answer: P(t)= __________________ (b) After 5 years, the amount in the account is $ __________ . (c) It takes ______ years for the investment to double. (d) It takes _____ years for the investment to reach $14,000.

a) 8000e^(0.051t) 🔑 8000*exp(0.051*t) b) 10,323.69 🔑 10,323.7 c) 13.59 🔑 13.6 d) 11 🔑 11