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
Question 2. Match the graph with its exponential function.
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
Question 5. Use the One-to-One property to solve the equation for x.
e3x+5 = 36
Question 6. Write the logarithmic equation in exponential form.
log8 64 = 2
Question 7. Write the logarithmic equation in exponential form.
log7 343 = 3
Question 8. Write the exponential equation in logarithmic form.
43 = 64
Question 9. Use the properties of logarithms to simplify the expression.
log20 209
Question 10. Use the One-to-One property to solve the equation for x.
log2(x+4) = log2 20
Question 11. Find the exact value of the logarithmic expression.
log6 36
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
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
Question 15. Determine whether the given x-value is a solution (or an approximate solution) of the equation.
42x-7 = 16
x = 5
Question 16. Solve for x.
3x = 81
Question 17. Solve the exponential equation algebraically. Approximate the resulte to three decimal places.
e5x = ex2-14
Question 18. Solve the logarithmic equation algebraically. Approximate the result to three decimal places.
log3(6x-8) = log3(5x + 10)
Question 19. Find the magnitude R of each earthquake of intensity I (let I0=1).
I = 19000
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
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