Math 1650.410 Midterm Exam 3 Review PDF

MATH 1650.410 Midterm Exam 3 Review Instructor: Pierce, Erin 1. Graph y = 3x and y = 3x−2. Note the differences in the two graphs. How do you get from one to the other? 2. Find the domain, range, and asymptote of the following functions:...

MATH 1650.410 Midterm Exam 3 Review Instructor: Pierce, Erin 1. Graph y = 3x and y = 3x−2. Note the differences in the two graphs. How do you get from one to the other? 2. Find the domain, range, and asymptote of the following functions: a)f (x) = 3x−2 b)f (x) = 2−x+1 c)f (x) = 3 + 2x d)f (x) = 5−x − 5 3. Write the equation in exponential form: a) log2 1024 = 10 b) log x = y 4. Write the equation in logarithmic form: a)26 = 64 b)10x = 74 5. Suppose that $12,000 is invested in a savings account paying 5.6% interest per year. How long will it take for the amount in the account to grow to $20,000 if interest is compounded continuously? 6. Find the exact value of the expression. a)10log 36 b) ln e3 √ c) log3 27 d) log2 80 − log2 10 e) log8 4 f ) log6 4 + log6 9 Page 1 of 3 MATH 1650.410 Midterm Exam 3 Review Instructor: Pierce, Erin 7. Use the Law of Logarithms to expand the expression.  3 xy a) log z2 r x b) ln y s x+2 c) log 3 4 2 x (x + 4) 8. The initial size of a culture of bacteria is 1000. After 1 hour the bacteria count is 8000. Find a function n(t) = n0 ert that models the population after t hours. 9. Find the function of the form y = loga x whose graph is given. a) b) 10. Use the Laws of Logarithms to combine the expression into a single logarithm. a) log a + 2 log b b) ln(x2 − 25) − ln(x + 5) 1 c) log2 3 − 3 log2 x + log2 (x + 1) 2 11. Find the solution of the exponential equation, rounded to two decimal places. a)34x = 3100 2 b)e3x−2 = ex c)5x/10 + 1 = 7 d)10x+3 = 62x 12. Solve the logarithmic equation for x. a) log(2x) = 3 b) log(x + 1) + log 2 = log(5x) c)5 ln(3 − x) = 4 d) log2 (x + 2) + log2 (x − 1) = 2 Page 2 of 3 MATH 1650.410 Midterm Exam 3 Review Instructor: Pierce, Erin 13. The graph shown below is one period of a function of the form y = a sin k(x − b). Determine the function. a) b) 14. Find the period and asymptotes of y = 3 tan x. 15. Find the period of y = tan(2x − π2 ). 16. Find the phase shift of y = 2 sin( 12 x − π6 ). 17. Find the exact value of the expression, if it is defined. a) tan−1 (tan 3π) √ b) cos(tan−1 (− 3)) Page 3 of 3