{"id":132,"date":"2026-01-12T15:50:00","date_gmt":"2026-01-12T15:50:00","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=132"},"modified":"2026-01-12T15:50:01","modified_gmt":"2026-01-12T15:50:01","slug":"exponential-and-logarithmic-functions-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/exponential-and-logarithmic-functions-get-stronger-answer-key\/","title":{"raw":"Exponential and Logarithmic Functions: Get Stronger Answer Key","rendered":"Exponential and Logarithmic Functions: Get Stronger Answer Key"},"content":{"raw":"

Exponential Functions<\/h2>\r\n
    \r\n \t
  1. exponential; the population decreases by a proportional rate.<\/li>\r\n \t
  2. not exponential; the charge decreases by a constant amount each visit, so the statement represents a linear function.<\/li>\r\n \t
  3. The forest represented by the function [latex]B(t)=82(1.029)^t[\/latex].<\/li>\r\n \t
  4. After [latex]t=20[\/latex] years, forest A will have [latex]43[\/latex] more trees than forest B.<\/li>\r\n \t
  5. exponential growth: The growth factor, [latex]1.06[\/latex], is greater than [latex]1[\/latex].<\/li>\r\n \t
  6. exponential decay: The decay factor, [latex]0.97[\/latex], is between [latex]0[\/latex] and [latex]1[\/latex].<\/li>\r\n \t
  7. [latex]f(x)=2000(0.1)^x[\/latex]<\/li>\r\n \t
  8. [latex]f(x)=(\\dfrac{1}{6})^{-\\frac{3}{5}}(\\dfrac{1}{6})^{\\frac{x}{5}}\\approx 2.93(0.699)^x[\/latex]<\/li>\r\n \t
  9. Linear<\/li>\r\n \t
  10. Neither<\/li>\r\n \t
  11. Linear<\/li>\r\n \t
  12. [latex]f(-1)=-4[\/latex]<\/li>\r\n \t
  13. [latex]f(-1)\\approx -0.2707[\/latex]<\/li>\r\n \t
  14. [latex]f(3)\\approx 483.8146[\/latex]<\/li>\r\n \t
  15. [latex]g(x)=4(3)^{-x}[\/latex]; [latex]y[\/latex]-intercept: [latex](0,4)[\/latex]; Domain: all real numbers; Range: all real numbers greater than [latex]0[\/latex].<\/li>\r\n \t
  16. [latex]g(x)=-10^x+7[\/latex]; [latex]y[\/latex]-intercept: [latex](0,6)[\/latex]; Domain: all real numbers; Range: all real numbers less than [latex]7[\/latex].<\/li>\r\n \t
  17. [latex]g(x)=2(\\dfrac{1}{4})^x[\/latex]; [latex]y[\/latex]-intercept: [latex](0,2)[\/latex]; Domain: all real numbers; Range: all real numbers greater than [latex]0[\/latex].<\/li>\r\n \t
  18. [latex]y[\/latex]-intercept: [latex](0,-2)[\/latex]\r\n\"Graph<\/li>\r\n \t
  19. \"Graph<\/li>\r\n \t
  20. B<\/li>\r\n \t
  21. A<\/li>\r\n \t
  22. E<\/li>\r\n \t
  23. D<\/li>\r\n \t
  24. C<\/li>\r\n \t
  25. [latex]f(x)=4^x-3[\/latex]<\/li>\r\n \t
  26. [latex]f(x)=4^{x-5}[\/latex]<\/li>\r\n \t
  27. [latex]f(x)=4^{-x}[\/latex]<\/li>\r\n \t
  28. [latex]y=-2^x+3[\/latex]<\/li>\r\n \t
  29. [latex]y=-2(3)^x+7[\/latex]<\/li>\r\n<\/ol>\r\n

    Applications of Exponential Functions<\/h2>\r\n
      \r\n \t
    1. [latex]$10,250[\/latex]<\/li>\r\n \t
    2. [latex]$13,268.58[\/latex]<\/li>\r\n \t
    3. [latex]P=A(t)\\cdot(1+\\dfrac{r}{n})^{-nt}[\/latex]<\/li>\r\n \t
    4. [latex]$4,572.56[\/latex]<\/li>\r\n \t
    5. [latex]4 \\%[\/latex]<\/li>\r\n \t
    6. continuous growth; the growth rate is greater than [latex]0[\/latex].<\/li>\r\n \t
    7. continuous decay; the growth rate is less than [latex]0[\/latex].<\/li>\r\n \t
    8. [latex]47,622[\/latex] fox<\/li>\r\n \t
    9. [latex]1.39 \\%[\/latex]; [latex]$155,368.09[\/latex]<\/li>\r\n \t
    10. [latex]$35,838.76[\/latex]<\/li>\r\n \t
    11. [latex]$82,247.78[\/latex]; [latex]$449.75[\/latex]<\/li>\r\n<\/ol>\r\n

      Logarithmic Functions<\/h2>\r\n
        \r\n \t
      1. [latex]a^c = b[\/latex]<\/li>\r\n \t
      2. [latex]x^y = 64[\/latex]<\/li>\r\n \t
      3. [latex]15^b = a[\/latex]<\/li>\r\n \t
      4. [latex]\\log_c(k) = d[\/latex]<\/li>\r\n \t
      5. [latex]\\log_{19}y = x[\/latex]<\/li>\r\n \t
      6. [latex]\\log_n(103) = 4[\/latex]<\/li>\r\n \t
      7. [latex]\\log_y(\\dfrac{39}{100}) = x[\/latex]<\/li>\r\n \t
      8. [latex]x = 2^{-3} = \\dfrac{1}{8}[\/latex]<\/li>\r\n \t
      9. [latex]x = 3^3 = 27[\/latex]<\/li>\r\n \t
      10. [latex]x = 9^{\\frac{1}{2}} = 3[\/latex]<\/li>\r\n \t
      11. [latex]32[\/latex]<\/li>\r\n \t
      12. [latex]1.06[\/latex]<\/li>\r\n \t
      13. [latex]14.125[\/latex]<\/li>\r\n \t
      14. [latex]\\dfrac{1}{2}[\/latex]<\/li>\r\n \t
      15. [latex]4[\/latex]<\/li>\r\n \t
      16. [latex]-3[\/latex]<\/li>\r\n \t
      17. [latex]-12[\/latex]<\/li>\r\n \t
      18. [latex]0[\/latex]<\/li>\r\n \t
      19. [latex]10[\/latex]<\/li>\r\n<\/ol>\r\n

        Logarithmic Function Graphs and Characteristics<\/h2>\r\n
          \r\n \t
        1. Domain: [latex](-\\infty,\\dfrac{1}{2})[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]<\/li>\r\n \t
        2. Domain: [latex](-\\dfrac{17}{4},\\infty)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]<\/li>\r\n \t
        3. Domain: [latex](5,\\infty)[\/latex]; Vertical asymptote: [latex]x=5[\/latex]<\/li>\r\n \t
        4. Domain: [latex](-\\dfrac{1}{3},\\infty)[\/latex]; Vertical asymptote: [latex]x=-\\dfrac{1}{3}[\/latex]<\/li>\r\n \t
        5. Domain: [latex](-3,\\infty)[\/latex]; Vertical asymptote: [latex]x=-3[\/latex]<\/li>\r\n \t
        6. Domain: [latex](1,\\infty)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]; Vertical asymptote: [latex]x=1[\/latex]; [latex]x[\/latex]-intercept: [latex](\\dfrac{5}{4},0)[\/latex]; [latex]y[\/latex]-intercept: DNE<\/li>\r\n \t
        7. Domain: [latex](-\\infty,0)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]; Vertical asymptote: [latex]x=0[\/latex]; [latex]x[\/latex]-intercept: [latex](-e^2,0)[\/latex]; [latex]y[\/latex]-intercept: DNE<\/li>\r\n \t
        8. Domain: [latex](0,\\infty)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]; Vertical asymptote: [latex]x=0[\/latex]; [latex]x[\/latex]-intercept: [latex](e^3,0)[\/latex]; [latex]y[\/latex]-intercept: DNE<\/li>\r\n \t
        9. B<\/li>\r\n \t
        10. C<\/li>\r\n \t
        11. B<\/li>\r\n \t
        12. C<\/li>\r\n \t
        13. \"Graph<\/li>\r\n \t
        14. \"Graph<\/li>\r\n \t
        15. \"Graph<\/li>\r\n \t
        16. \"Graph<\/li>\r\n \t
        17. \"Graph<\/li>\r\n \t
        18. [latex]f(x)=\\log_2(-x-1)[\/latex]<\/li>\r\n \t
        19. [latex]f(x)=3\\log_4(x+2)[\/latex]<\/li>\r\n<\/ol>","rendered":"

          Exponential Functions<\/h2>\n
            \n
          1. exponential; the population decreases by a proportional rate.<\/li>\n
          2. not exponential; the charge decreases by a constant amount each visit, so the statement represents a linear function.<\/li>\n
          3. The forest represented by the function [latex]B(t)=82(1.029)^t[\/latex].<\/li>\n
          4. After [latex]t=20[\/latex] years, forest A will have [latex]43[\/latex] more trees than forest B.<\/li>\n
          5. exponential growth: The growth factor, [latex]1.06[\/latex], is greater than [latex]1[\/latex].<\/li>\n
          6. exponential decay: The decay factor, [latex]0.97[\/latex], is between [latex]0[\/latex] and [latex]1[\/latex].<\/li>\n
          7. [latex]f(x)=2000(0.1)^x[\/latex]<\/li>\n
          8. [latex]f(x)=(\\dfrac{1}{6})^{-\\frac{3}{5}}(\\dfrac{1}{6})^{\\frac{x}{5}}\\approx 2.93(0.699)^x[\/latex]<\/li>\n
          9. Linear<\/li>\n
          10. Neither<\/li>\n
          11. Linear<\/li>\n
          12. [latex]f(-1)=-4[\/latex]<\/li>\n
          13. [latex]f(-1)\\approx -0.2707[\/latex]<\/li>\n
          14. [latex]f(3)\\approx 483.8146[\/latex]<\/li>\n
          15. [latex]g(x)=4(3)^{-x}[\/latex]; [latex]y[\/latex]-intercept: [latex](0,4)[\/latex]; Domain: all real numbers; Range: all real numbers greater than [latex]0[\/latex].<\/li>\n
          16. [latex]g(x)=-10^x+7[\/latex]; [latex]y[\/latex]-intercept: [latex](0,6)[\/latex]; Domain: all real numbers; Range: all real numbers less than [latex]7[\/latex].<\/li>\n
          17. [latex]g(x)=2(\\dfrac{1}{4})^x[\/latex]; [latex]y[\/latex]-intercept: [latex](0,2)[\/latex]; Domain: all real numbers; Range: all real numbers greater than [latex]0[\/latex].<\/li>\n
          18. [latex]y[\/latex]-intercept: [latex](0,-2)[\/latex]
            \n\"Graph<\/li>\n
          19. \"Graph<\/li>\n
          20. B<\/li>\n
          21. A<\/li>\n
          22. E<\/li>\n
          23. D<\/li>\n
          24. C<\/li>\n
          25. [latex]f(x)=4^x-3[\/latex]<\/li>\n
          26. [latex]f(x)=4^{x-5}[\/latex]<\/li>\n
          27. [latex]f(x)=4^{-x}[\/latex]<\/li>\n
          28. [latex]y=-2^x+3[\/latex]<\/li>\n
          29. [latex]y=-2(3)^x+7[\/latex]<\/li>\n<\/ol>\n

            Applications of Exponential Functions<\/h2>\n
              \n
            1. [latex]$10,250[\/latex]<\/li>\n
            2. [latex]$13,268.58[\/latex]<\/li>\n
            3. [latex]P=A(t)\\cdot(1+\\dfrac{r}{n})^{-nt}[\/latex]<\/li>\n
            4. [latex]$4,572.56[\/latex]<\/li>\n
            5. [latex]4 \\%[\/latex]<\/li>\n
            6. continuous growth; the growth rate is greater than [latex]0[\/latex].<\/li>\n
            7. continuous decay; the growth rate is less than [latex]0[\/latex].<\/li>\n
            8. [latex]47,622[\/latex] fox<\/li>\n
            9. [latex]1.39 \\%[\/latex]; [latex]$155,368.09[\/latex]<\/li>\n
            10. [latex]$35,838.76[\/latex]<\/li>\n
            11. [latex]$82,247.78[\/latex]; [latex]$449.75[\/latex]<\/li>\n<\/ol>\n

              Logarithmic Functions<\/h2>\n
                \n
              1. [latex]a^c = b[\/latex]<\/li>\n
              2. [latex]x^y = 64[\/latex]<\/li>\n
              3. [latex]15^b = a[\/latex]<\/li>\n
              4. [latex]\\log_c(k) = d[\/latex]<\/li>\n
              5. [latex]\\log_{19}y = x[\/latex]<\/li>\n
              6. [latex]\\log_n(103) = 4[\/latex]<\/li>\n
              7. [latex]\\log_y(\\dfrac{39}{100}) = x[\/latex]<\/li>\n
              8. [latex]x = 2^{-3} = \\dfrac{1}{8}[\/latex]<\/li>\n
              9. [latex]x = 3^3 = 27[\/latex]<\/li>\n
              10. [latex]x = 9^{\\frac{1}{2}} = 3[\/latex]<\/li>\n
              11. [latex]32[\/latex]<\/li>\n
              12. [latex]1.06[\/latex]<\/li>\n
              13. [latex]14.125[\/latex]<\/li>\n
              14. [latex]\\dfrac{1}{2}[\/latex]<\/li>\n
              15. [latex]4[\/latex]<\/li>\n
              16. [latex]-3[\/latex]<\/li>\n
              17. [latex]-12[\/latex]<\/li>\n
              18. [latex]0[\/latex]<\/li>\n
              19. [latex]10[\/latex]<\/li>\n<\/ol>\n

                Logarithmic Function Graphs and Characteristics<\/h2>\n
                  \n
                1. Domain: [latex](-\\infty,\\dfrac{1}{2})[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]<\/li>\n
                2. Domain: [latex](-\\dfrac{17}{4},\\infty)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]<\/li>\n
                3. Domain: [latex](5,\\infty)[\/latex]; Vertical asymptote: [latex]x=5[\/latex]<\/li>\n
                4. Domain: [latex](-\\dfrac{1}{3},\\infty)[\/latex]; Vertical asymptote: [latex]x=-\\dfrac{1}{3}[\/latex]<\/li>\n
                5. Domain: [latex](-3,\\infty)[\/latex]; Vertical asymptote: [latex]x=-3[\/latex]<\/li>\n
                6. Domain: [latex](1,\\infty)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]; Vertical asymptote: [latex]x=1[\/latex]; [latex]x[\/latex]-intercept: [latex](\\dfrac{5}{4},0)[\/latex]; [latex]y[\/latex]-intercept: DNE<\/li>\n
                7. Domain: [latex](-\\infty,0)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]; Vertical asymptote: [latex]x=0[\/latex]; [latex]x[\/latex]-intercept: [latex](-e^2,0)[\/latex]; [latex]y[\/latex]-intercept: DNE<\/li>\n
                8. Domain: [latex](0,\\infty)[\/latex]; Range: [latex](-\\infty,\\infty)[\/latex]; Vertical asymptote: [latex]x=0[\/latex]; [latex]x[\/latex]-intercept: [latex](e^3,0)[\/latex]; [latex]y[\/latex]-intercept: DNE<\/li>\n
                9. B<\/li>\n
                10. C<\/li>\n
                11. B<\/li>\n
                12. C<\/li>\n
                13. \"Graph<\/li>\n
                14. \"Graph<\/li>\n
                15. \"Graph<\/li>\n
                16. \"Graph<\/li>\n
                17. \"Graph<\/li>\n
                18. [latex]f(x)=\\log_2(-x-1)[\/latex]<\/li>\n
                19. [latex]f(x)=3\\log_4(x+2)[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":106,"module-header":"- Select Header -","content_attributions":[],"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\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/132"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/132\/revisions"}],"predecessor-version":[{"id":140,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/132\/revisions\/140"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/106"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/132\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=132"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=132"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=132"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}