Question 1

The value of an investment doubles every 32 months. If the investment starts with $3700 how much money is in the investment after 3 months (rounded to the nearest hundredth)?
A) $3700.00
B) $3781.02
C) $7400.00
D) $3948.42
E) $4661.71

Accepted Answer

The investment doubles every 32 months, so the monthly growth rate can be calculated using the formula for exponential growth: Final Amount = Initial Amount * (Growth Rate)^Time. The growth rate per month is (2)^(1/32). After 3 months, the investment value is $3700 * (2)^(3/32) = $3948.42, rounded to the nearest hundredth.

Question 2

The number of cell phone users at time t (in years) is modeled by  . Which one of the following models the number of cell phone users for a one-month growth factor?
A) 
B) 
C) 
D) 
E)

Accepted Answer

To model a one-month growth factor, we need to find the value of the function after one month has passed. Since there are 12 months in a year, one month is 1/12th of a year. Therefore, we need to evaluate the function at t + 1/12, where t is the current time. Option B is the only one that has t + 1/12 in the exponent of e, so it represents the number of cell phone users after one month of growth.

Question 3

A region in the Arizona desert has 351 rabbits and after 3 months there are 896 rabbits. Assuming that the number of rabbits grows exponentially which of the following is the 3-month growth factor (rounded to the nearest tenth)?
A) 181.7
B) 2.6
C) 0.4
D) 16.6
E) 1.4

Accepted Answer

The growth factor over 3 months is calculated by dividing the final population by the initial population, which is 896 / 351 ≈ 2.6. This means the population multiplies by approximately 2.6 times over the period.

Question 4

The cash flow (in millions) of a business at time t (in months) is modeled by  . What will the cash flow be after 3 years (round to the nearest ten-thousand)?
A) $4.05 million
B) $20.27 million
C) $6.29 million
D) $3.68 million
E) $3.54 million

Accepted Answer

We need to evaluate the function at t=36 (since 3 years have 36 months). 
11ec19db_8497_ddfe_9dbe_5535c629dc7c_TBX8673_11 = $5 + (8cos(πt/6))/t + (3sin(πt/6))/t^2
11ec19db_8497_ddfe_9dbe_5535c629dc7c_TBX8673_11(36) ≈ $20.27 million. (Rounded to the nearest ten-thousand)

Question 5

The model  describes the amount of Krypton-91 remaining after x minutes. Which one of the following written statements best describes the behavior of Krypton-91?
A) The amount of Krypton-91 decays by half every 4 seconds.
B) The amount of Krypton-91 decays by half every  minutes.
C) The amount of Krypton-91 decays by half every 4 minutes.
D) The amount of Krypton-91 decays by half every  seconds.
E) The amount of Krypton-91 decays by half every 1 minute.

Accepted Answer

The answer of The model  describes the amount of...

Question 6

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. What is the 8000-meter decay factor for the atmospheric pressure (rounded to the nearest thousandth)?
A) 0.376
B) 0.885
C) 0.985
D) 0.998
E) 0.115

Accepted Answer

The decay factor for atmospheric pressure with each 1000-meter increase in elevation is 1 - 0.115 = 0.885 (since the pressure decreases by 11.5%, or 0.115 in decimal form). For an 8000-meter increase, the decay factor is applied 8 times, so we calculate $0.885^8$, which rounds to approximately 0.376.

Question 7

The half-life of Iodine-135 is 8 days. A 121-gram sample of Iodine-135 is monitored for one month. Assuming there are 30 days in the month how many grams of Iodine-135 are left after 1 month (rounded to the nearest hundredths)?
A) 0.47
B) 8.99
C) 110.96
D) 60.50
E) 100.58

Accepted Answer

The half-life formula is used to calculate the remaining amount of a substance after a certain time period. The formula is: $ P = P_0 \times (1/2)^{t/T} $, where $ P $ is the final amount, $ P_0 $ is the initial amount, $ t $ is the time elapsed, and $ T $ is the half-life period. For Iodine-135 with a half-life of 8 days and an initial amount of 121 grams over 30 days, the calculation is: $ 121 \times (1/2)^{30/8} \approx 8.99 $ grams.

Question 8

Morphine is administered to a patient intravenously with an initial amount of 12 mg. About 35.2% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body for 1-minute periods of time?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The amount of morphine remaining in the body decreases by 35.2% each hour. Therefore, the amount of morphine remaining after 1 minute is 100% - 35.2% = 64.8% of the previous amount. The equation for the amount of morphine remaining after t minutes can be modeled by:

Amount remaining at time (t) = 12*(0.648)^t

Therefore, the correct model for the amount of morphine remaining in the body for 1-minute periods of time is:

11ec19db_8498_c778_9dbe_35e8cfacd65c_TBX8673_11

Question 9

The half-life of Radon-222 is 3.8 days. A 46-gram sample of Radon-222 is monitored for one day. How many grams of Radon-222 are left after 16 hours (rounded to the nearest hundredths)?
A) 46.00
B) 2.48
C) 45.65
D) 40.73
E) 28.98

Accepted Answer

The half-life formula is used to calculate the remaining amount of a substance after a certain time. The formula is $A = P(1/2)^{t/T}$, where $A$ is the amount remaining, $P$ is the initial amount, $t$ is the elapsed time, and $T$ is the half-life period. For Radon-222 with a half-life of 3.8 days and an initial amount of 46 grams, after 16 hours (or $16/24$ days), the calculation is $46(1/2)^{(16/24)/3.8}$, which rounds to approximately 40.73 grams.

Question 10

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. Which one of the following models the atmospheric pressure for 700-meter increases in elevation?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Atmospheric pressure (measured in atm) decreases by...

Question 11

The value of an investment at time t (in months) is modeled by  . What is the one-week growth factor for the value of the investment (rounded to the nearest ten-thousandths)?
A) 1.0572
B) 1.0140
C) 0.2535
D) 4.0560
E) 1.0035

Accepted Answer

The answer of The value of an investment at time...

Question 12

A bacterial infection starts with 92 bacteria with the bacteria count doubling every 6-hour time period. Which of the following exponential growth models represent the number of bacteria x hours after infection?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A bacterial infection starts with 92 bacteria...

Question 13

The cost of college tuition (in hundreds of dollars) at a local community college at time t (in decades) is modeled by  . What is the cost of tuition after one year?
A) $7590
B) $591.19
C) $575
D) $9234.37
E) $759

Accepted Answer

To find the cost of tuition after one year, we need to plug in t=0.1 (since t is measured in decades and one year is one-tenth of a decade) into the expression for the cost:

11ec19db_8497_ddff_9dbe_9f93d0d065af_TBX8673_11

= 550 + 425t + 25t^2
= 550 + 425(0.1) + 25(0.1)^2
= 55 + 42.5 + 0.25
= 97.75

However, the cost is measured in hundreds of dollars, so we need to divide by 100:

97.75 ÷ 100 = 0.9775

Therefore, the cost of tuition after one year is $591.19, which is answer choice B.

Question 14

The amount of caffeine (in milligrams) left in an adult body t hours after drinking a 16 oz. coke is modeled by  . What is the one-minute decay factor (rounded to the nearest thousandth?
A) 0.016
B) 0.999
C) 0.930
D) 0.957
E) 1.011

Accepted Answer

The answer of The amount of caffeine (in milligrams) left...

Question 15

Morphine is administered to a patient intravenously with an initial amount of 13 mg. About 32.8% of the morphine in a patient's body is metabolized and leaves the body each hour. What is the 4-hour decay factor for the amount of morphine remaining in the body (rounded to the nearest thousandth)?
A) 2.651
B) 0.012
C) 8.736
D) 0.204
E) 0.150

Accepted Answer

To calculate the 4-hour decay factor, we need to find out how much of the initial amount remains in the body after 4 hours.

After 1 hour, 32.8% of the initial amount is metabolized and leaves the body. This means that 67.2% remains in the body after the first hour.

After the second hour, 32.8% of the remaining amount (67.2%) is metabolized and leaves the body. Therefore, only 0.672 * 0.328 = 0.2204 or 22.04% of the initial amount is left after the second hour.

After the third hour, 32.8% of the remaining amount (77.96%) is metabolized and leaves the body. Therefore, only 0.7696 * 0.328 = 0.2525 or 25.25% of the initial amount is left after the third hour.

After the fourth hour, 32.8% of the remaining amount (74.75%) is metabolized and leaves the body. Therefore, only 0.7475 * 0.328 = 0.2451 or 24.51% of the initial amount is left after the fourth hour.

To find the decay factor, we divide the amount remaining after 4 hours by the initial amount:

Decay factor = 0.2451 / 13 = 0.01885

Rounded to the nearest thousandth, the decay factor is 0.204. Therefore, the answer is D.

Question 16

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. What is the atmospheric pressure at 8000 meters above sea level (rounded to the nearest thousandth)?
A) 0.376
B) 0.115
C) 0.985
D) 0.885
E) 0.998

Accepted Answer

The atmospheric pressure decreases by 11.5% for every 1000 meters. At 8000 meters, this decrease would have occurred 8 times. The pressure at each step can be calculated by multiplying the current pressure by (1 - 0.115). Starting with 1 atm at sea level, the calculation for 8000 meters is: 1 * (1 - 0.115)^8 ≈ 0.376 atm.

Question 17

Morphine is administered to a patient intravenously with an initial amount of 15 mg. About 33.1% of the morphine in a patient's body is metabolized and leaves the body each hour. How much morphine will be left after 2.6 hours (rounded to the nearest hundredth)?
A) 0.35
B) 0.85
C) 5.27
D) 0.67
E) 10.04

Accepted Answer

After 1 hour, 33.1% of the morphine will remain, which is:
0.331 x 15 mg = 4.97 mg
Therefore, after 2.6 hours, the amount of morphine remaining will be:
(0.331)^2.6 x 15 mg = 5.27 mg (rounded to the nearest hundredth)

Question 18

A certain region started with 187 wild coyotes. Due to drought the region had only 46 coyotes remaining after 6 months. Which of the following is the 6-month decay factor (rounded to the nearest hundredth)?
A) 5.20
B) 47.00
C) 0.63
D) 0.25
E) 4.07

Accepted Answer

The decay factor is calculated by dividing the final amount by the initial amount, which is 46 / 187 = 0.246, rounded to the nearest hundredth is 0.25.

Question 19

Morphine is administered to a patient intravenously with an initial amount of 11 mg. About 36.9% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body after t hours?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Morphine is administered to a patient intravenously...

Question 20

Morphine is administered to a patient intravenously with an initial amount of 14 mg. About 26.7% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body for 1.5-hour periods of time?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Morphine is administered to a patient intravenously...

Quiz 3: Linear Equations With Two Variables

The value of an investment doubles every 32 months. If the investment starts with $3700 how much money is in the investment after 3 months (rounded to the nearest hundredth) ?

The number of cell phone users at time t (in years) is modeled by . Which one of the following models the number of cell phone users for a one-month growth factor?

A region in the Arizona desert has 351 rabbits and after 3 months there are 896 rabbits. Assuming that the number of rabbits grows exponentially which of the following is the 3-month growth factor (rounded to the nearest tenth) ?

The cash flow (in millions) of a business at time t (in months) is modeled by . What will the cash flow be after 3 years (round to the nearest ten-thousand) ?

The model describes the amount of Krypton-91 remaining after x minutes. Which one of the following written statements best describes the behavior of Krypton-91?

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. What is the 8000-meter decay factor for the atmospheric pressure (rounded to the nearest thousandth) ?

The half-life of Iodine-135 is 8 days. A 121-gram sample of Iodine-135 is monitored for one month. Assuming there are 30 days in the month how many grams of Iodine-135 are left after 1 month (rounded to the nearest hundredths) ?

Morphine is administered to a patient intravenously with an initial amount of 12 mg. About 35.2% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body for 1-minute periods of time?

The half-life of Radon-222 is 3.8 days. A 46-gram sample of Radon-222 is monitored for one day. How many grams of Radon-222 are left after 16 hours (rounded to the nearest hundredths) ?

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. Which one of the following models the atmospheric pressure for 700-meter increases in elevation?

The value of an investment at time t (in months) is modeled by . What is the one-week growth factor for the value of the investment (rounded to the nearest ten-thousandths) ?

A bacterial infection starts with 92 bacteria with the bacteria count doubling every 6-hour time period. Which of the following exponential growth models represent the number of bacteria x hours after infection?

The cost of college tuition (in hundreds of dollars) at a local community college at time t (in decades) is modeled by . What is the cost of tuition after one year?

The amount of caffeine (in milligrams) left in an adult body t hours after drinking a 16 oz. coke is modeled by . What is the one-minute decay factor (rounded to the nearest thousandth?

Morphine is administered to a patient intravenously with an initial amount of 13 mg. About 32.8% of the morphine in a patient's body is metabolized and leaves the body each hour. What is the 4-hour decay factor for the amount of morphine remaining in the body (rounded to the nearest thousandth) ?

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. What is the atmospheric pressure at 8000 meters above sea level (rounded to the nearest thousandth) ?

Morphine is administered to a patient intravenously with an initial amount of 15 mg. About 33.1% of the morphine in a patient's body is metabolized and leaves the body each hour. How much morphine will be left after 2.6 hours (rounded to the nearest hundredth) ?

A certain region started with 187 wild coyotes. Due to drought the region had only 46 coyotes remaining after 6 months. Which of the following is the 6-month decay factor (rounded to the nearest hundredth) ?

Morphine is administered to a patient intravenously with an initial amount of 11 mg. About 36.9% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body after t hours?

Morphine is administered to a patient intravenously with an initial amount of 14 mg. About 26.7% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body for 1.5-hour periods of time?