Question

1. the equation below shows that the value of a $6,000 certificate of deposit (cd) n years in the future will be $6,700. what is the approximate amount of time that must pass before the cd will have a value of $6,700?

$6,700 = 6,000 (1 + 0.026)^n$

a) 5.1 years
b) 4.6 years
c) 5.2 years
d) 2.6 years

1. the equation below shows that the value of a $5,000 certificate of deposit (cd) n years in the future will be $5,600. what is the approximate amount of time that must pass before the cd will have a value of $5,600?

$5,600 = 5,000 (1 + 0.03)^n$

a) 4.2 years
b) 4.9 years
c) 3.8 years
d) 2.6 years

1. survey results for the political race of county commissioner in a small town show that 42% of those surveyed plan to vote for john doe, 46% plan to vote for sue smith, and 12% of voters are undecided. the survey sample size is 625 and the margin of error is 4%. which of the following statements about this scenario are true? select two that apply.

a) because of the margin of error, the candidates are tied and neither candidate can be predicted to win.
b) sue smith will win the county commissioner race since a higher percentage of voters surveyed plan to vote for her.
c) if the undecided voters were split evenly between the two candidates, then john doe could beat sue smith for the county commissioner position.
d) the margin of error accounts for the randomness of the sample selected.

1. $log_{4} 4^{2}$

a) 1
b) 2
c) 4
d) 16

1. $ln e^{-2}$

a) -2
b) 4
c) 1
d) -4

Explanation:

Step1: Simplify the equation

Divide both sides by 6000: $\frac{6700}{6000} = (1 + 0.025)^n \Rightarrow 1.1167 \approx 1.025^n$

Step2: Take log of both sides

$\log(1.1167) = n\log(1.025)$

Step3: Solve for n

$n = \frac{\log(1.1167)}{\log(1.025)} \approx \frac{0.0479}{0.0107} \approx 4.5$

Step1: Simplify the equation

Divide both sides by 5000: $\frac{5600}{5000} = (1 + 0.03)^n \Rightarrow 1.12 = 1.03^n$

Step2: Take log of both sides

$\log(1.12) = n\log(1.03)$

Step3: Solve for n

$n = \frac{\log(1.12)}{\log(1.03)} \approx \frac{0.0492}{0.0128} \approx 3.8$

• Statement a: John's interval is 42±4=38-46%, Sue's is 46±4=42-50%. Overlap means no clear winner. True.
• Statement b: Cannot predict win due to interval overlap. False.
• Statement c: Undecided split evenly: John=42+9=51%, Sue=46+9=55% (Sue still leads). False.
• Statement d: Margin of error accounts for sampling randomness. True.

Step1: Apply log power rule

$\log_4 4^{27} = 27\log_4 4$

Step2: Simplify $\log_4 4$

$\log_4 4 = 1$, so $27×1=27$

Answer:

B. 4.6 years