4?88%- ASK YOUR TEACHER 2:22 PM Sat Oct 15 webassignnel m 42. [/0.32 Points] SPRECALC7 4.5.090.MI. 0/5 Submissions Used A woman invests $5500 in an account that pays 6% interest per year, compounded continuously. (a) What is the amount after 2 years? (Round your answer to the nearest cent.) $ :l (b) How long will it take for the amount to be $10,000? (Round your answer to two decimal places.) :JV' Need Help? 43. [/0.56 Points] SPRECALC7 4.5.098.MI. 0/5 Submissions Used ASK YOUR TEACHER Environmental scientists measure the intensity of light at various depths in a lake to find the "transparency" of the water. Certain levels of transparency are required for the biodiversity of the submerged macrophyte population. In a certain lake the intensity of light at depth x is given by I = 2e0.003x where I is measured in lumens and x in feet. (a) Find the intensity I at a depth of 15 ft. (Round your answer to two decimal places.) (b) At what depth has the light intensity dropped to I = 1? (Round your answer to one decimal place.) [:1 ft Need Help? _'__' 2:20 PM Sat Oct 15 . . . 1 89% webassign.net 17. [-/0.32 Points] DETAILS SPRECALC7 4.4.058.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to combine the expression. loga(b) + c loga(d) - r loga(s) Need Help? Read It Master It Submit Answer 18. [-/0.32 Points] DETAILS SPRECALC7 4.4.062.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. log6(93) Need Help? Read It Master It 19. [-/0.32 Points] DETAILS SPRECALC7 4.4.070.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Simplify: (log7(3))(1093(8)). Need Help? Read It Watch It Master It 20. [-/0.32 Points] DETAILS SPRECALC7 4.4.074.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Some biologists model the number of species S in a fixed area A (such as an island) by the species-area relationship log(S) = log(c) + k log(A) where c and k are positive constants that depend on the type of species and habitat.B. [IO.32 Points] DETAILS SPRECALC7 4.4.502.XP.M|. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to expand the expression. '095(X(X - 5)) Need Help? \" 9. [0/032 Points] DETAILS PREVIOUS ANSWERS 1/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to expand the expression. X lo 7 985 Submit Answer 10. [-/0.32 Points] DETAILS 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to expand the expression. In v3 Sr7s 20. [-l0.32 Points] DETAILS SPRECALC7 4.4.074.M|. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Some biologists model the number of species Sin a fixed area A (such as an island) by the species-area relationship log(S) = Iog(c) + k log(A) where c and k are positive constants that depend on the type of species and habitat. (a) Solve the equation for S. S= (b) Using part (a), if k = 2 and the area is tripled, then by what magnitude is the number of species increased? Need Help? 21. [-/0.32 Points] DETAILS SPRECALC7 4.5.001. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Let's solve the exponential equation 3ex = 45. (a) First, we isolate e" to get the equivalent equation (b) Next, we take In of each side to get the equivalent equation (c) Now we use a calculator to find x z E. (Round your answer to t1ree decimal places.) Need Help? 1. [ID.32 Points] DETAILS SPRECALC7 4.4.006. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER (a) Most calculators can find logarithms With base land base e. To find logarithms with different bases, we use the; following. (Round your answers to three decimal places.) W2) Mi [:1) (b) Do we get the same answer if we perform the calculation in part (a) using In in place of log? 0 Yes, the result is the same. Ebbinghaus' Law O No, the result is not the same. Of Forgetting _ To find log7(8), we write the \\/ --Select-- \" [2 Change of Base Formula Laws of Logarithms |097(8) = Need Help? Common Logarithm Formula Submit Answer 22. [/0.32 Points] DETAILS SPRECALC7 4.5.002. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Let's solve the logarithmic equation log(3) + log(X 7 2) = log(x). (a) First, we combine the logarithms on the LHS to get the equivalent equation = log(x). (b) Next, we use the fact that log is one-to-one to get the equivalent equation = x. (c) Now we nd x = :1. Need Help? 11. [/0.32 Points] DETAILS 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws 0 Logarithms to expand the expression. Ig( big/E) 12. [-/0.32 Points] DETAILS SPRECALC7 4.4.511.XP.M|. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to expand the expression. memo/E) Neee Help? 13. [-/0.32 Points] DETAILS SPRECALC7 4.4.048.M|. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to expand the expression. Iog( Xv y/E) Need Help? 14. [0/0.32 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 4.4.515.XP.MI. 1/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to combine the expression. log (81) + = log (2) - 109(9 ) X Need Help? Read It Master It Submit Answer 15. [-/0.32 Points] DETAILS SPRECALC7 4.4.054.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to combine the expression. 1092 ( x 2 - 4) - 1092 ( x - 2 ) Need Help? Read It Master It 16. [-/0.32 Points] DETAILS SPRECALC7 4.4.055.MI. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER Use the Laws of Logarithms to combine the expression. In(a + b) + In(a - b) - 8 In(c) Need Help? Read It Watch It Master It