Question 1

Lisinopril is an ACE inhibitor derived from the venom of a Brazilian pit viper frequently used in the treatment of hypertension. Because of Lisinopril's relatively long half-life of 12 hours, patients need to take a dose just once per day. A patient takes his first dose, 20 mg, at 6 pm on Saturday.
a) How many hours does it take for the amount of Lisinopril in the patient's body to decrease to 17 mg? Round to two decimal places.
b) How many milligrams remain in the patient's body right before he takes his next 20 mg at 6 pm on Sunday? Round to two decimal places

Accepted Answer

The answer of Lisinopril is an ACE inhibitor derived from...

Question 2

A quantity growing exponentially according to the formula  has a doubling time of  .

Accepted Answer

The doubling time for an exponential growth formula of the form A*2^(t/k) is given by the formula k*ln 2. Therefore, in this case, the doubling time is ln 2/11eb69ff_fedc_7647_af94_2d57d61bd97f_TB8190_11, which is a constant. This means that the quantity in question is growing exponentially with a constant doubling time, so the statement is true.

Question 3

A standard cup of coffee contains about 100 mg of caffeine, and caffeine leaves the body at a rate of about 17% an hour. How many mg of caffeine are left in the body after 6 hours if this rate is continuous? Round to 2 decimal places.

Accepted Answer

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Question 4

Is the function described by the following table of values exponential?

Accepted Answer

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Question 5

An exponentially decaying substance was weighed every hour and the results are given below. What is the half-life of the substance? Round to the nearest tenth.

Accepted Answer

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Question 6

The population  of the United States in millions t years after 1790 during the period from 1790 to 1860 was given approximately by the exponential formula  . What was the annual percent growth rate of the US during this time period?

Accepted Answer

The answer of The population  of the United States...

Question 7

The population of Nicaragua was 3.6 million in 1990 and growing at 3.4% per year. Let P be the population in millions, and let t be the time in years since 1990. Express P as a function of t. Select all that apply.
A) 
B) 
C) 
D)

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The answer of The population of Nicaragua was 3.6 million...

Question 8

If the size of a bacteria colony doubles in 8 hours, how many hours will it take for the number of bacteria to be 11 times the original amount? Round to 2 decimal places.

Accepted Answer

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Question 9

In the book One Grain of Rice, a girl receives a reward that starts with one grain of rice on day one, two grains on day two, four on day three and eight on day four. Each day, she receives double the number of grains of rice. How many grains of rice does she receive on the 20th day?
A)400
B)1,048,576
C)2,782,184
D)40

Accepted Answer

To find the amount of rice on the 20th day, we need to keep doubling the amount from the previous day. So, on the 20th day, she would have received 2^19 grains of rice (since we started with one grain on day one). 2^19 is equal to 1,048,576, so the answer is B.

Question 10

A new species, introduced into an environment in which it has no natural predators, grows exponentially with continuous growth rate k=0.095 per year. There are initially 45 individuals introduced. Write the formula for  , the number of individuals after t years and use it to find how many years will it take for the population to reach 300 individuals. Round to 2 decimal places.

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Question 11

Suppose $1200 is invested at 10% annual interest and $1500 is invested at 8% annual interest. After how many years will the investments be equal? Round to the nearest whole number.

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Question 12

In 1992, the Population Crisis Committee wrote:
"Large cities in developing countries are growing much faster than cities in the industrialized world ever have. London, which in 1810 became the first industrialized city to top 1 million, now has a population of 11 million. By contrast, Mexico City's population stood at only a million just 50 years ago and now it is 20 million."
Assume that the percentage growth rates of London and Mexico City were constant over the last two centuries. How many times greater is Mexico City's percentage growth rate than London's? Round to the nearest tenth.

Accepted Answer

The answer of In 1992, the Population Crisis Committee wrote:
"Large...

Question 13

An exponentially decaying substance was weighed every hour and the results are given below. If the formula  gives the weight of the substance, Q, at time t in hours since 9 am, then  =_____ and k=_____. Round k to 2 decimal points.

Accepted Answer

The answer of An exponentially decaying substance was weighed every...

Question 14

If  , find and simplify the average rate of change  .
A)1
B) 
C) 
D)

Accepted Answer

To find the average rate of change, we need to subtract the initial value from the final value and divide by the change in input. In this case, the initial value is 11eb69ff_fedc_c469_af94_7b159fc1b2fe_TB8190_11 and the final value is 11eb69ff_fedc_eb7d_af94_a54a6eda465b_TB8190_11. The change in input is the difference between the last four digits, which is 0x7d - 0x69 = 0x14 = 20 in decimal. Therefore, the average rate of change is (11eb69ff_fedc_eb7d_af94_a54a6eda465b_TB8190_11 - 11eb69ff_fedc_c469_af94_7b159fc1b2fe_TB8190_11) / 20 = 11eb69ff_fedc_eb7d_af94_a54a6eda465b_TB8190_11.

Question 15

The population of Nicaragua was 3.6 million in 1990 and growing at 3.4% per year. How many years does it take for the population of Nicaragua to increase by 60%? Round to 2 decimal places.

Accepted Answer

The answer of The population of Nicaragua was 3.6 million...

Question 16

A standard cup of coffee contains about 100 mg of caffeine, and caffeine leaves the body at a rate of about 17% an hour. How many mg of caffeine are left in the body after 6 hours if this rate is hourly? Round to 2 decimal places.

Accepted Answer

The answer of A standard cup of coffee contains about...

Question 17

A clean up of a polluted lake will remove 4% of the remaining contaminants every year. How many years will it take to reduce the quantity of contaminants to 1/10 of its present level? Round to the nearest tenth.

Accepted Answer

The answer of A clean up of a polluted lake...

Question 18

A cigarette contains about 0.4 mg of nicotine. The half-life of nicotine in the body is about 2 hours. How many hours does it take, after smoking a cigarette, for the level of nicotine in a smoker's body to be reduced to 0.1 mg? Round to 2 decimal places.

Accepted Answer

The answer of A cigarette contains about 0.4 mg of...

Question 19

The population  of the United States in millions t years after 1790 during the years from 1790 to 1860 was given approximately by the exponential formula  . What was the approximate doubling time for the population? Round to the nearest year.

Accepted Answer

The answer of The population  of the United States...

Question 20

Which is worth more after 10 years: $1200 invested at 10% annual interest or $1500 invested at 8% annual interest?
A)The 8% investment
B)The 10% investment

Accepted Answer

The answer of Which is worth more after 10 years:...

Quiz 1: Functions and Change

A quantity growing exponentially according to the formula has a doubling time of .

A standard cup of coffee contains about 100 mg of caffeine, and caffeine leaves the body at a rate of about 17% an hour. How many mg of caffeine are left in the body after 6 hours if this rate is continuous? Round to 2 decimal places.

Is the function described by the following table of values exponential?

An exponentially decaying substance was weighed every hour and the results are given below. What is the half-life of the substance? Round to the nearest tenth.

The population of the United States in millions t years after 1790 during the period from 1790 to 1860 was given approximately by the exponential formula . What was the annual percent growth rate of the US during this time period?

The population of Nicaragua was 3.6 million in 1990 and growing at 3.4% per year. Let P be the population in millions, and let t be the time in years since 1990. Express P as a function of t. Select all that apply.

If the size of a bacteria colony doubles in 8 hours, how many hours will it take for the number of bacteria to be 11 times the original amount? Round to 2 decimal places.

In the book One Grain of Rice, a girl receives a reward that starts with one grain of rice on day one, two grains on day two, four on day three and eight on day four. Each day, she receives double the number of grains of rice. How many grains of rice does she receive on the 20th day?

Suppose $1200 is invested at 10% annual interest and $1500 is invested at 8% annual interest. After how many years will the investments be equal? Round to the nearest whole number.

An exponentially decaying substance was weighed every hour and the results are given below. If the formula gives the weight of the substance, Q, at time t in hours since 9 am, then =_ and k=_. Round k to 2 decimal points.

If , find and simplify the average rate of change .

The population of Nicaragua was 3.6 million in 1990 and growing at 3.4% per year. How many years does it take for the population of Nicaragua to increase by 60%? Round to 2 decimal places.

A standard cup of coffee contains about 100 mg of caffeine, and caffeine leaves the body at a rate of about 17% an hour. How many mg of caffeine are left in the body after 6 hours if this rate is hourly? Round to 2 decimal places.

A clean up of a polluted lake will remove 4% of the remaining contaminants every year. How many years will it take to reduce the quantity of contaminants to 1/10 of its present level? Round to the nearest tenth.

A cigarette contains about 0.4 mg of nicotine. The half-life of nicotine in the body is about 2 hours. How many hours does it take, after smoking a cigarette, for the level of nicotine in a smoker's body to be reduced to 0.1 mg? Round to 2 decimal places.

The population of the United States in millions t years after 1790 during the years from 1790 to 1860 was given approximately by the exponential formula . What was the approximate doubling time for the population? Round to the nearest year.

Which is worth more after 10 years: $1200 invested at 10% annual interest or $1500 invested at 8% annual interest?