This week you were introduced to the natural number e

Question

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

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

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