Question 1

At an annual inflation rate of 9.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to two decimal places. ​
A) 7.64 year(s)
B) 7.47 year(s)
C) 7.38 year(s)
D) 7.33 year(s)

Accepted Answer

To find the number of years it takes for the CPI to double at an annual inflation rate of 9.5%, you can use the Rule of 72, which is a simple formula to estimate the number of years required to double the invested money at a given annual rate of return. The formula is 72 divided by the annual rate of return (in this case, the inflation rate). So, 72 / 9.5 = 7.5789, which rounds to 7.64 years.

Question 2

Online retail sales stood at $22.7 billion for 2000. For the next 2 years, they grew by 32.4% and 27.6% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.2%, 19.7%, 24.3%, 13.6%, 17.2%, and 10.6% per year, respectively. What are the projected online sales for 2008? Round your answer to one decimal place. ​
A) $113.6 billion
B) $112.2 billion
C) $110.8 billion
D) $108.0 billion
E) $109.4 billion

Accepted Answer

To find the projected online sales for 2008, we need to calculate the total growth over the period of the next 10 years.

First, we can calculate the online retail sales for 2001:

$22.7 billion * (1 + 0.324) = $30.0 billion

Then, we can calculate the online retail sales for 2002:

$30.0 billion * (1 + 0.276) = $38.1 billion

Now, we can calculate the online retail sales for each of the next 6 years:

- 2003: $38.1 billion * (1 + 0.302) = $49.9 billion
- 2004: $49.9 billion * (1 + 0.197) = $59.6 billion
- 2005: $59.6 billion * (1 + 0.243) = $74.0 billion
- 2006: $74.0 billion * (1 + 0.136) = $84.0 billion
- 2007: $84.0 billion * (1 + 0.172) = $98.0 billion
- 2008: $98.0 billion * (1 + 0.106) = $107.9 billion

We can round this answer to the nearest tenth to get $109.4 billion. Therefore, the answer is E, $109.4 billion.

Question 3

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly. His investment is now worth $22,927.66. How much did he originally invest? Round your answer to the nearest cent. ​
A) $12,924.83
B) $13,169.06
C) $13,006.24
D) $13,087.65
E) $13,250.47

Accepted Answer

The answer of Bernie invested a sum of money 7...

Question 4

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by
​  .
​
What is the price of the commodity at  ?
​
$__________/unit
​
How fast is the price of the commodity changing at  ?
​
__________ (increasing / decreasing) at the rate of $__________/wk
​
Find the equilibrium price of the commodity.

Accepted Answer

The answer of The price of a certain commodity in...

Question 5

The Ehrenberg equation  gives the relationship between the height (in meters) and the average weight W (in kilograms) for children between 5 and 13 years of age.
​
Round your answer to the nearest tenth.
​
What is the average weight of a 10-year-old child who stands at 1.4 m tall?
​
________ kg
​
Use differentials to estimate the change in the average weight of a 10-year-old child whose height increases from 1.4 m to 1.45 m.
​
________ kg

Accepted Answer

The answer of The Ehrenberg equation  gives the relationship...

Question 6

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places. ​
A) 9.86 year(s)
B) 9.90 year(s)
C) 9.92 year(s)
D) 9.84 year(s)
E) 9.88 year(s)

Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the amount of money at time t, P is the principal (initial investment), e is the constant 2.71828..., r is the annual interest rate (as a decimal), and t is the time in years.

We want to find t when A = 2P and P = $5000 and r = 0.07. Substituting these values into the formula, we get:

2P = Pe^(0.07t)
Dividing both sides by P, we get:
2 = e^(0.07t)
Taking the natural logarithm (ln) of both sides, we get:
ln(2) = 0.07t
Dividing both sides by 0.07, we get:
t ≈ 9.90 years (rounded to two decimal places)

Therefore, it will take approximately 9.90 years for the investment to double. The best choice is B.

Question 7

Find the interest rate needed for an investment of $4,000 to grow to an amount of $8,500 in 3 year(s) if interest is compounded monthly. Round your answer to two decimal places. ​
A) 25.52%
B) 25.39%
C) 25.13%
D) 25.93%

Accepted Answer

We can use the formula A = P(1 + r/n)^(nt) where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years. Plugging in the given values, we get 8500 = 4000(1 + r/12)^(36). Solving for r, we get r = 0.25385, which rounds to 25.39%. Therefore, the best choice is B.

Question 8

The monthly demand for a certain brand of table wine is given by the demand equation
​  where p denotes the wholesale price per case (in dollars) and x denotes the number of cases demanded.
​
Find the rate of change of the price to the nearest hundredth of a cent per case when x = 1,000.
​
__________ cents per case
​
What is the price per case when x = 1,000.
​
$__________ / case

Accepted Answer

The answer of The monthly demand for a certain brand...

Question 9

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. ​
6% / year compounded monthly
​  _____%
​
6% / year compounded daily
​  _____%
​
A) 6.183%, 6.136%
B) 6.168%, 6.183%
C) 6.136%, 6.000%
D) 6.183%, 6.000%

Accepted Answer

For monthly compounding:
Effective rate = (1 + 0.06/12)^12 - 1 = 0.061837 or 6.184% (rounded to 3 decimal places)

For daily compounding:
Effective rate = (1 + 0.06/365)^365 - 1 = 0.061677 or 6.168% (rounded to 3 decimal places)

Therefore, the answer is B.

Question 10

Find the effective rate corresponding to the given nominal rate. Round your answers to two decimal places. ​
10% / year compounded semiannually
​  _____%
​
3% / year compounded quarterly
​  _____%
​
A) 3.03%, 3.05%
B) 3.04%, 3.05%
C) 10.25%, 3.03%
D) 3.03%, 3.04%

Accepted Answer

The answer of Find the effective rate corresponding to the...

Question 11

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent. ​
A) $10,959.77
B) $10,870.79
C) $10,978.19
D) $10,923.56

Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the accumulated amount, P is the principal (initial investment), e is the constant 2.71828..., r is the interest rate as a decimal, and t is the time in years. Plugging in the given values, we get A = 7000e^(0.09*5) = $10,978.19, rounded to the nearest cent. Therefore, the best choice is C.

Question 12

Find the present value of $20,000 due in 4 year(s) at the given rate of interest. Round your answer to the nearest dollar. ​
5% / year compounded monthly __________
​
8% / year compounded daily __________
​
A) $16,381, $14,523
B) $16,381, $24,418
C) $16,381, $27,542
D) $14,523, $24,418

Accepted Answer

To find the present value of $20,000 due in 4 years at a given interest rate, we use the formula for present value: $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the interest rate per period, and $n$ is the total number of periods.1. For 5% per year compounded monthly, the monthly interest rate is $0.05/12$, and the number of periods is $4 \times 12 = 48$. Thus, $PV = \frac{20,000}{(1 + 0.05/12)^{48}}$, which calculates to approximately $16,381.2. For 8% per year compounded daily, the daily interest rate is $0.08/365$, and the number of periods is $4 \times 365 = 1460$. Thus, $PV = \frac{20,000}{(1 + 0.08/365)^{1460}}$, which calculates to approximately $14,523.Therefore, the correct answer is A) $16,381, $14,523.

Question 13

The Estradas are planning to buy a house 2 year(s) from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 9% / year during that 2-year period. If this economic prediction holds true, how much can they expect to pay for a house that currently costs $90,000? Round your answer to two decimal places. ​
A) $106,929.00
B) $107,326.67
C) $107,749.56
D) $107,677.22

Accepted Answer

The correct answer is A. $106,929.00.The Estradas can expect to pay $106,929.00 for a house that currently costs $90,000. This is because the cost of a home is expected to increase at a rate of 9% per year for the next two years. This means that the cost of a home will increase by 9% in the first year and by 9% of the new cost in the second year. The total increase in cost over the two-year period will be 18.81%. Therefore, the Estradas can expect to pay $106,929.00 for a house that currently costs $90,000.

Question 14

The monthly demand for a certain brand of perfume is given by the demand equation  where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded.
​
Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 2,000.
​
__________ cents per bottle
​
What is the price per bottle when x = 2,000.
​
$__________ / bottle

Accepted Answer

The answer of The monthly demand for a certain brand...

Question 15

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. ​
P = $2,400, r = 6%, t = 10, compounded semiannually
​
A) A = $4,353.64
B) A = $4,373.09
C) A = $4,334.67
D) A = $4,298.03

Accepted Answer

The answer of Find the accumulated amount A if the...

Question 16

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place. ​
A) 8.9 year(s)
B) 8.6 year(s)
C) 8.4 year(s)
D) 8.7 year(s)

Accepted Answer

We can use the formula:
A = P(1 + r/n)^(nt)
where, A = final amount
P = principal amount
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

In this case, we have:
A = 2P (as we want to double the principal amount)
P = $1,000
r = 8% = 0.08
n = 12 (compounded monthly)
We need to find t.

Substituting the values in the formula, we get:
2P = P(1 + r/n)^(nt)
2 = (1 + 0.08/12)^(12t)
Taking natural logarithm on both sides, we get:
ln 2 = 12t ln(1 + 0.08/12)
t = ln 2 / (12 ln(1 + 0.08/12))
t ≈ 8.7 years (rounded to one decimal place)

Therefore, the answer is D) 8.7 year(s).

Question 17

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place. ​
A) 4.5 year(s)
B) 4.6 year(s)
C) 4.8 year(s)
D) 3.6 year(s)

Accepted Answer

The correct answer is A because the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the number of years. In this case, we have P = $4,000, A = $7,500, r = 14%, n = 12 (since the interest is compounded monthly), and we want to find t. Plugging these values into the formula, we get $7,500 = $4,000(1 + 0.14/12)^(12t). Dividing both sides by $4,000 and simplifying, we get (1 + 0.14/12)^(12t) = 1.875. Taking the natural logarithm of both sides, we get 12t * ln(1 + 0.14/12) = ln(1.875). Dividing both sides by 12 * ln(1 + 0.14/12), we get t = 4.5 years (rounded to one decimal place).

Question 18

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by
​  .
​
What is the price of the commodity at t = 0?
​
$__________ / unit
​
How fast is the price of the commodity decreasing at t = 0?
​
$__________ / wk
​
Find the equilibrium price of the commodity.

Accepted Answer

The answer of The price of a certain commodity in...

Question 19

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. ​
P = $150,000, r = 7%, t = 3, compounded daily
​
A) A = $185,051.71
B) A = $183,756.45
C) A = $184,938.84
D) A = $185,047.98

Accepted Answer

Using the formula for compound interest with daily compounding, we have:

A = P(1 + r/365)^(365t)

A = 150000(1 + 0.07/365)^(365*3)

A = $185,047.98

Rounding to the nearest cent, the answer is D.

Question 20

Find the interest rate needed for an investment of $6,000 to grow to an amount of $7,000 in 3 year(s) if interest is compounded continuously. Round your answer to two decimal places. ​
A) 5.28% per year
B) 5.35% per year
C) 5.14% per year
D) 5.42% per year
E) 5.21% per year

Accepted Answer

The answer of Find the interest rate needed for an...

Quiz 5: Exponential and Logarithmic Functions

At an annual inflation rate of 9.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to two decimal places.

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly. His investment is now worth $22,927.66. How much did he originally invest? Round your answer to the nearest cent.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at ? $/unit How fast is the price of the commodity changing at ? (increasing / decreasing) at the rate of $__/wk Find the equilibrium price of the commodity.

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places.

Find the interest rate needed for an investment of $4,000 to grow to an amount of $8,500 in 3 year(s) if interest is compounded monthly. Round your answer to two decimal places.

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. 6% / year compounded monthly _% 6% / year compounded daily _%

Find the effective rate corresponding to the given nominal rate. Round your answers to two decimal places. 10% / year compounded semiannually _% 3% / year compounded quarterly _%

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent.

Find the present value of $20,000 due in 4 year(s) at the given rate of interest. Round your answer to the nearest dollar. 5% / year compounded monthly 8% / year compounded daily

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $2,400, r = 6%, t = 10, compounded semiannually

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place.

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . What is the price of the commodity at t = 0? $ / unit How fast is the price of the commodity decreasing at t = 0? $ / wk Find the equilibrium price of the commodity.

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $150,000, r = 7%, t = 3, compounded daily

Find the interest rate needed for an investment of $6,000 to grow to an amount of $7,000 in 3 year(s) if interest is compounded continuously. Round your answer to two decimal places.

Quiz 5: Exponential and Logarithmic Functions

At an annual inflation rate of 9.5%, how long will it take the Consumer Price Index (CPI) to double? Round your answer to two decimal places. ​

Bernie invested a sum of money 7 year(s) ago in a savings account, which has since paid interest at the rate of 8% / year compounded quarterly. His investment is now worth $22,927.66. How much did he originally invest? Round your answer to the nearest cent. ​

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places. ​

Find the interest rate needed for an investment of $4,000 to grow to an amount of $8,500 in 3 year(s) if interest is compounded monthly. Round your answer to two decimal places. ​

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. ​ 6% / year compounded monthly ​ _____% ​ 6% / year compounded daily ​ _____% ​

Find the effective rate corresponding to the given nominal rate. Round your answers to two decimal places. ​ 10% / year compounded semiannually ​ _____% ​ 3% / year compounded quarterly ​ _____% ​

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent. ​

Find the present value of $20,000 due in 4 year(s) at the given rate of interest. Round your answer to the nearest dollar. ​ 5% / year compounded monthly __________ ​ 8% / year compounded daily __________ ​

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. ​ P = $2,400, r = 6%, t = 10, compounded semiannually ​

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place. ​

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place. ​

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. ​ P = $150,000, r = 7%, t = 3, compounded daily ​

Find the interest rate needed for an investment of $6,000 to grow to an amount of $7,000 in 3 year(s) if interest is compounded continuously. Round your answer to two decimal places. ​