Question 1

Find the number of digits in the given number.

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Question 2

Find an integer k such that 19^k has 308 digits.

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Question 3

Find the smallest integer k such that 
  
 .

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The answer of Find the smallest integer k such that...

Question 4

Find the smallest integer M such that  
 .
A) 69,315
B) 69,316
C) 0
D) 2

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Question 5

For x = 9 and y = 8, evaluate each of the following. Round your answer to four decimal places. A) log(x^y) b) (log x)^y

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Question 6

Evaluate    . Round your answer to four decimal places.

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Question 7

Evaluate    . Round your answer to four decimal places.

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Question 8

About how many years will it take for a sample of plutonium-239 to have only   as much plutonium-239 as the original sample?

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Question 9

About how many years will it take for a sample of polonium-210 to have at most 7% as much polonium-210 as the original sample?
A) 530 years
B) 2 years
C) 1 year
D) 529 years

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Question 10

Suppose a radioactive isotope is such that   of the atoms in a sample decay after 6 years. How many years is the half-life of this isotope? Round your answer to the nearest tenth.

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Question 11

A human bone is founded in your backyard. The ratio of carbon-14 to carbon-12 in the bone is 40% at the corresponding ratio for living organisms. Calculate the age of the bone.
A) 5,250 years
B) 30,495 years
C) 7,575 years
D) 5,729 years

Accepted Answer

The half-life of carbon-14 is approximately 5,730 years. If the ratio is 40%, it means the bone has gone through more than one half-life. Using the formula for radioactive decay, the age is approximately 7,575 years.

Question 12

Evaluate the indicated expression.

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 ...

Question 13

Evaluate the indicated expression. 
A) 3/2
B) 3
C) 2/3
D) 1/2

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A) 3/2
B) 3
C)...

Question 14

Evaluate the indicated expression. 
A) 6
B) 0.33
C) 3
D) 12

Accepted Answer

The answer of Evaluate the indicated expression. 
A) 6
B) 0.33
C)...

Question 15

Evaluate the indicated expression. 
A) 3/2
B) -3/2
C) 2/3
D) -2/3

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The answer of Evaluate the indicated expression. 
A) 3/2
B) -3/2
C)...

Question 16

Find a number y such that   .

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Question 17

Find a number t such that  .
A) 256
B) 0.0039
C) -256
D) -0.0039

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Question 18

Find a number b such that the indicated equality holds.

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Question 19

Find a number x such that    . Round your answer to two decimal places.

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Question 20

Find a number t such that    . Round your answer to four decimal places.

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Quiz 4: Exponential Functions, Logarithms, and E

Find the number of digits in the given number.

Find an integer k such that 19k has 308 digits.

Find the smallest integer k such that .

Find the smallest integer M such that .

For x = 9 and y = 8, evaluate each of the following. Round your answer to four decimal places. A) log(xy) b) (log x)y

Evaluate . Round your answer to four decimal places.

Evaluate . Round your answer to four decimal places.

About how many years will it take for a sample of plutonium-239 to have only as much plutonium-239 as the original sample?

About how many years will it take for a sample of polonium-210 to have at most 7% as much polonium-210 as the original sample?

Suppose a radioactive isotope is such that of the atoms in a sample decay after 6 years. How many years is the half-life of this isotope? Round your answer to the nearest tenth.

A human bone is founded in your backyard. The ratio of carbon-14 to carbon-12 in the bone is 40% at the corresponding ratio for living organisms. Calculate the age of the bone.

Evaluate the indicated expression.

Evaluate the indicated expression.

Evaluate the indicated expression.

Evaluate the indicated expression.

Find a number y such that .

Find a number t such that .

Find a number b such that the indicated equality holds.

Find a number x such that . Round your answer to two decimal places.

Find a number t such that . Round your answer to four decimal places.

Find an integer k such that 19^k has 308 digits.

For x = 9 and y = 8, evaluate each of the following. Round your answer to four decimal places. A) log(x^y) b) (log x)^y