Question

1. )A machine can lift a weight of 10 kg on the first day. The weight it can lift increases by 20 percent each day. How much weight can the machine lift on the fifth day? Round your answer to two decimal places. (1 point)

20.01 kg

20.74 kg

22.44 kg

22.54 kg

2. )A car dealer sold 100 cars in his first year and plans to increase his sales by 10 percent each year for the next 5 years. How many cars will he have sold at the end of his fifth year?(1 point)

1,245

920

725

610

3. )What is the sum of the first seven terms of a series whose first term is 2 and has a common ratio of 4?(1 point)

922

10,922

11,022

4. )An annuity account earns biannual payments (e.g. two payments per year) and has an annual interest rate of 5 percent. What value of r must be substituted into the formula to calculate the future value of the annuity? Round the value to the nearest thousandth.(1 point)

0.004

0.001

0.025

0.050

5. )What would the n value be for an annuity that has weekly payments for two years? There are 52 weeks in a year.(1 point)

24

12

104

52

6. )Shane wants to save for a down payment on a house and plans to deposit $700 every month into an annuity for the next 7 years. If the annuity interest rate is 5 percent per year, what is the present value of the annuity? Round your answer to the nearest hundredth.(1 point)

$49,526.28

$48,345.16

$49,985.64

$48,678.12

7. )A bacteria colony starts with 10 cells. Each hour a biologist adds triple the number of cells. In the geometric series model, of the total number of bacteria, what is the first term?(1 point)

3

10

8

4

8. )A man invests $1,000 in a bank account. Each year, he increases the amount he deposits into the account by 15%. What will be the total amount of money in the account after 7 years? Round to the nearest whole number. (1 point)

$9,587

$10,227

$11,067

$8,125

9. )What value should replace r in sigma notation to find the sum of the first 8 terms of the sequence −2,−8,−32, . . .?(1 point)

4

−32

8

-2

10. )An annuity account earns payments every other month and has an annual interest rate of 14 percent. What value of r must be substituted into the formula to calculate the future value of the annuity? Round the value to the nearest thousandth.(1 point)

0.003

0.140

0.070

0.023

11. )Which formula can be adapted to calculate the future value of an annuity?







(1 point)

the sum of a finite geometric series

the sum of an infinite geometric series

the sum of an infinite arithmetic series

the sum of a finite arithmetic series

12. )Write the sigma notation for the geometric series from the following finite geometric sequence: 100, 80, 64.(1 point)


∑3n=1100(0.8)n−1



∑3n=1100(3)n−1





∑100n=13(0.8)n−1


∑3n=11.2(100)n−1

13. )Which of the following is the sum of the first five terms of the geometric series whose first term is a and that has a common ratio of 2r?(1 point)



S5=α−32αr5(1+2r)



S5=a−2ar5(1−2r)

S5=a−32ar5(1−r)

S5=a−32ar5(1−2r)

14. )You decide you want to buy a house in 5 years and need to have a down payment of $75,000. A high yield money market account has an annual interest rate of 7 percent. Which calculation would you use to determine if a monthly deposit of $300.00 would be enough to reach your goal?(1 point)

FV=300(1−.00583)60+1.00583

FV=300(1+.00583)5−1.00583

FV=300(1+.00583)60−1.00583

FV=300(1+.07)60−1.07

Answer 1

1. 20.74 kg (10*(1.2)^4 = 20.736 → 20.74)

2. 610 (cumulative sales after 5 years: 100*(1.1^5 − 1)/0.1 ≈ 610)

3. 10,922 (S7 = 2*(4^7 − 1)/(4 − 1) = 10,922)

4. 0.025 (period rate = 0.05/2)

5. 104 (n = 2 years * 52 weeks)

6. $49,526.28 (PV of monthly $700 for 7 years at 5% annual ≈ $49,526.28)

7. 10 (first term = initial 10 cells)

8. $11,067 (sum = 1000*(1.15^7 − 1)/0.15 ≈ $11,067)

9. 4 (common ratio = (−8)/(−2) = 4)

10. 0.023 (period rate = 0.14/6 ≈ 0.023)

11. the sum of a finite geometric series

12. ∑_{n=1}^{3} 100(0.8)^{n−1}

13. S5 = (a − 32 a r^5)/(1 − 2r) (i.e. a*(1 − (2r)^5)/(1 − 2r))

14. FV = 300((1 + 0.00583)^{60} − 1)/0.00583 (the option corresponding to this formula)