{"id":285,"date":"2025-02-13T22:46:03","date_gmt":"2025-02-13T22:46:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/solutions-exponential-and-logarithmic-functions-practice-test\/"},"modified":"2025-02-13T22:46:03","modified_gmt":"2025-02-13T22:46:03","slug":"solutions-exponential-and-logarithmic-functions-practice-test","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/solutions-exponential-and-logarithmic-functions-practice-test\/","title":{"raw":"Solutions: Exponential and Logarithmic Functions Practice Test","rendered":"Solutions: Exponential and Logarithmic Functions Practice Test"},"content":{"raw":"\n1. About 13 dolphins.\n\n3. $1,947\n\n5. y<\/em>-intercept: (0, 5)\n\"Graph\n\n7. [latex]{8.5}^{a}=614.125[\/latex]\n\n9. [latex]x={\\left(\\frac{1}{7}\\right)}^{2}=\\frac{1}{49}[\/latex]\n\n11. [latex]\\mathrm{ln}\\left(0.716\\right)\\approx -0.334[\/latex]\n\n13. Domain: x <\/em>< 3; Vertical asymptote: x <\/em>= 3; End behavior: [latex]x\\to {3}^{-},f\\left(x\\right)\\to -\\infty [\/latex] and [latex]x\\to -\\infty ,f\\left(x\\right)\\to \\infty [\/latex]\n\n15. [latex]{\\mathrm{log}}_{t}\\left(12\\right)[\/latex]\n\n17. [latex]3\\mathrm{ln}\\left(y\\right)+2\\mathrm{ln}\\left(z\\right)+\\frac{\\mathrm{ln}\\left(x - 4\\right)}{3}[\/latex]\n\n19. [latex]x=\\frac{\\frac{\\mathrm{ln}\\left(1000\\right)}{\\mathrm{ln}\\left(16\\right)}+5}{3}\\approx 2.497[\/latex]\n\n21. [latex]a=\\frac{\\mathrm{ln}\\left(4\\right)+8}{10}[\/latex]\n\n23. no solution\n\n25. [latex]x=\\mathrm{ln}\\left(9\\right)[\/latex]\n\n27. [latex]x=\\pm \\frac{3\\sqrt{3}}{2}[\/latex]\n\n29. [latex]f\\left(t\\right)=112{e}^{-.019792t}[\/latex]; half-life: about 35 days\n\n31. [latex]T\\left(t\\right)=36{e}^{-0.025131t}+35;T\\left(60\\right)\\approx {43}^{\\text{o}}\\text{F}[\/latex]\n\n33. logarithmic\n\"Graph\n\n35. exponential; [latex]y=15.10062{\\left(1.24621\\right)}^{x}[\/latex]\n\"Graph\n\n37. logistic; [latex]y=\\frac{18.41659}{1+7.54644{e}^{-0.68375x}}[\/latex]\n\"Graph\n","rendered":"

1. About 13 dolphins.<\/p>\n

3. $1,947<\/p>\n

5. y<\/em>-intercept: (0, 5)
\n\"Graph<\/p>\n

7. [latex]{8.5}^{a}=614.125[\/latex]<\/p>\n

9. [latex]x={\\left(\\frac{1}{7}\\right)}^{2}=\\frac{1}{49}[\/latex]<\/p>\n

11. [latex]\\mathrm{ln}\\left(0.716\\right)\\approx -0.334[\/latex]<\/p>\n

13. Domain: x <\/em>< 3; Vertical asymptote: x <\/em>= 3; End behavior: [latex]x\\to {3}^{-},f\\left(x\\right)\\to -\\infty[\/latex] and [latex]x\\to -\\infty ,f\\left(x\\right)\\to \\infty[\/latex]<\/p>\n

15. [latex]{\\mathrm{log}}_{t}\\left(12\\right)[\/latex]<\/p>\n

17. [latex]3\\mathrm{ln}\\left(y\\right)+2\\mathrm{ln}\\left(z\\right)+\\frac{\\mathrm{ln}\\left(x - 4\\right)}{3}[\/latex]<\/p>\n

19. [latex]x=\\frac{\\frac{\\mathrm{ln}\\left(1000\\right)}{\\mathrm{ln}\\left(16\\right)}+5}{3}\\approx 2.497[\/latex]<\/p>\n

21. [latex]a=\\frac{\\mathrm{ln}\\left(4\\right)+8}{10}[\/latex]<\/p>\n

23. no solution<\/p>\n

25. [latex]x=\\mathrm{ln}\\left(9\\right)[\/latex]<\/p>\n

27. [latex]x=\\pm \\frac{3\\sqrt{3}}{2}[\/latex]<\/p>\n

29. [latex]f\\left(t\\right)=112{e}^{-.019792t}[\/latex]; half-life: about 35 days<\/p>\n

31. [latex]T\\left(t\\right)=36{e}^{-0.025131t}+35;T\\left(60\\right)\\approx {43}^{\\text{o}}\\text{F}[\/latex]<\/p>\n

33. logarithmic
\n\"Graph<\/p>\n

35. exponential; [latex]y=15.10062{\\left(1.24621\\right)}^{x}[\/latex]
\n\"Graph<\/p>\n

37. logistic; [latex]y=\\frac{18.41659}{1+7.54644{e}^{-0.68375x}}[\/latex]
\n\"Graph<\/p>\n","protected":false},"author":6,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":276,"module-header":"","content_attributions":[{"type":"cc","description":"Precalculus","author":"Jay Abramson, et al.","organization":"OpenStax","url":"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175","project":"","license":"cc-by","license_terms":"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175."}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/285"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/285\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/276"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/285\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=285"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=285"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=285"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}