Introduced to the natural number

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Reference no: EM131092959

This week you were introduced to the natural number e ≈ 2.718. In mathematics there are several important numbers similar to e. You are likely familiar with the constant pi ≈ 3.14. For example: You are likely familiar with the constant pi ≈ 3.14.

  • Do some research on either one of these two numbers, or, better yet, find another very important number in mathematics.
  • Share with us what you have found out about the number, for example, its history, some trivial facts about the number, and/or how it is applied.

Question 1. Evaluate the function at the indicated value of x.  Round your result to three decimal places.

Function: f(x) = 0.5x   Value: x = 1.7


-0.308


1.7


0.308


0.5


-1.7

Question 2. Match the graph with its exponential function.


y = 2-x - 3


y = -2x + 3


y = 2x + 3


y = 2x - 3


y = -2x - 3

Question 3. Select the graph of the function.

f(x) = 5x-1

202_ku.jpg

1558_ku.jpg

Question 4. Evaluate the function at the indicated value of x.  Round your result to three decimal places.

Function: f(x) = 500e0.05x    Value: x=17


1169.823


1369.823


1569.823


1269.823


1469.823

Question 5. Use the One-to-One property to solve the equation for x.

e3x+5 = 36


x = -1/3


x2 = 6


x = -3


x = 1/3


x = 3

Question 6. Write the logarithmic equation in exponential form.

log8 64 = 2


648 = 2


82 = 16


82 = 88


82 = 64


864 = 2

Question 7. Write the logarithmic equation in exponential form.

log7 343 = 3


7343 = 2


73 = 77


73 = 343


73 = 14


3437 = 2

Question 8. Write the exponential equation in logarithmic form.

43 = 64


log64 4 = 3


log4 64 = 3


log4 64 = -3


log4 3 = 64


log4 64 = 1/3

Question 9. Use the properties of logarithms to simplify the expression.

log20 209


0


-1/9


1/9


-9


9

Question 10. Use the One-to-One property to solve the equation for x.

log2(x+4) = log2 20


19


17


18


16


20

Question 11. Find the exact value of the logarithmic expression.

log6 36


2


6


36


-2


none of these

Question 12. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.  (Assume all variables are positive.)

log3 9x


log3 9/log3 x


log3 9 x log3 x


log3 9 + log3 x


log3 9 log3


none of these

Question 13. Condense the expression to a logarithm of a single quantity. 

logx - 2logy + 3logz

1704_ku.jpg

Question 14. Evaluate the logarithm using the change-of-base formula.  Round your result to three decimal places.

log4 9


1.585


5.585


3.585


4.585


2.585

Question 15. Determine whether the given x-value is a solution (or an approximate solution) of the equation.

42x-7 = 16

x = 5


no


yes

Question 16. Solve for x.

3x = 81


7


3


4


-4


-3

Question 17. Solve the exponential equation algebraically.  Approximate the resulte to three decimal places.

e5x = ex2-14


-7, -2


7, -2


5, -14


7, 2


-7, 2

Question 18. Solve the logarithmic equation algebraically.  Approximate the result to three decimal places.

log3(6x-8) = log3(5x + 10)


18


20


17


19


-2

Question 19. Find the magnitude R of each earthquake of intensity I (let I0=1).

I = 19000


3.28


5.28


4.28


2.38


6.28

Question 20. $2500 is invested in an account at interest rate r, compounded continuously.  Find the time required for the amount to double.  (Approximate the result to two decimal places.)

r = 0.0570


13.16 years


10.16 years


11.16 years


12.16 years


14.16 years

Reference no: EM131092959

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