[
  {
    "Question": "What is the value of log2(32)?",
    "Answer": "C",
    "Explanation": "log2(32) means 'to what power must 2 be raised to get 32?' Since 2^5 = 32, the answer is 5.",
    "PictureURL": "",
    "OptionA": "4",
    "OptionB": "5",
    "OptionC": "6",
    "OptionD": "7",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Logarithmic Functions",
    "Item": 1,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "If a population of bacteria doubles every 3 hours, how many hours will it take for the population to grow from 100 to 800?",
    "Answer": "B",
    "Explanation": "The population doubles every 3 hours: 100 -> 200 (3 hours), 200 -> 400 (6 hours), 400 -> 800 (9 hours). So, it takes 9 hours.",
    "PictureURL": "",
    "OptionA": "6 hours",
    "OptionB": "9 hours",
    "OptionC": "12 hours",
    "OptionD": "15 hours",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Population Growth",
    "Item": 2,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the formula for continuous compound interest?",
    "Answer": "A",
    "Explanation": "The formula for continuous compound interest is A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.",
    "PictureURL": "",
    "OptionA": "A = Pe^(rt)",
    "OptionB": "A = P(1 + r/n)^(nt)",
    "OptionC": "A = P(1 + r)^t",
    "OptionD": "A = P(1 - r)^t",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Compound Interest",
    "Item": 3,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "If a radioactive substance has a half-life of 5 years, how much of a 100g sample remains after 15 years?",
    "Answer": "B",
    "Explanation": "After 15 years (which is 3 half-lives), the remaining amount is 100g / 2^3 = 100g / 8 = 12.5g.",
    "PictureURL": "",
    "OptionA": "25g",
    "OptionB": "12.5g",
    "OptionC": "50g",
    "OptionD": "75g",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Half-Life Calculation",
    "Item": 4,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the inverse of the function f(x) = 3^x?",
    "Answer": "C",
    "Explanation": "The inverse of an exponential function f(x) = a^x is a logarithmic function. Therefore, the inverse is f^(-1)(x) = log3(x).",
    "PictureURL": "",
    "OptionA": "log2(x)",
    "OptionB": "log10(x)",
    "OptionC": "log3(x)",
    "OptionD": "3^(-x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse Functions",
    "Item": 5,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "If an investment of $1000 grows to $2000 in 5 years, what is the annual growth rate assuming continuous compounding?",
    "Answer": "A",
    "Explanation": "Using the formula A = Pe^(rt), we can rearrange to find r. Here, 2000 = 1000e^(5r), leading to r = ln(2)/5 ≈ 0.1386 or 13.86%.",
    "PictureURL": "",
    "OptionA": "13.86%",
    "OptionB": "10%",
    "OptionC": "15%",
    "OptionD": "20%",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Growth Rate Calculation",
    "Item": 6,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the value of e^0?",
    "Answer": "B",
    "Explanation": "Any number raised to the power of 0 is 1, so e^0 = 1.",
    "PictureURL": "",
    "OptionA": "0",
    "OptionB": "1",
    "OptionC": "e",
    "OptionD": "undefined",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Exponential Functions",
    "Item": 7,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "How long will it take for an investment to triple if it earns an annual interest rate of 5% compounded annually?",
    "Answer": "C",
    "Explanation": "Using the rule of 72, we can estimate that it will take about 72/5 = 14.4 years to triple.",
    "PictureURL": "",
    "OptionA": "10 years",
    "OptionB": "12 years",
    "OptionC": "14.4 years",
    "OptionD": "15 years",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Investment Growth",
    "Item": 8,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the logarithmic form of the equation 5^x = 25?",
    "Answer": "D",
    "Explanation": "The logarithmic form of an exponential equation a^b = c is log_a(c) = b. Here, log_5(25) = x.",
    "PictureURL": "",
    "OptionA": "log_5(5) = x",
    "OptionB": "log_5(25) = 2",
    "OptionC": "log_5(25) = x",
    "OptionD": "log_5(25) = 2",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Logarithmic Form",
    "Item": 9,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "If a population of 5000 grows at a rate of 4% per year, what will be the population after 10 years using the formula P = P0e^(rt)?",
    "Answer": "A",
    "Explanation": "Using the formula P = 5000e^(0.04*10), we find P ≈ 5000e^0.4 ≈ 5000 * 1.4918 ≈ 7459.",
    "PictureURL": "",
    "OptionA": "7459",
    "OptionB": "7000",
    "OptionC": "8000",
    "OptionD": "6000",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Population Growth Calculation",
    "Item": 10,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the base of the natural logarithm?",
    "Answer": "B",
    "Explanation": "The base of the natural logarithm is e, which is approximately equal to 2.71828.",
    "PictureURL": "",
    "OptionA": "10",
    "OptionB": "e",
    "OptionC": "2",
    "OptionD": "3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Natural Logarithm",
    "Item": 11,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "If a car depreciates in value by 15% each year, what will be its value after 3 years if it starts at $20,000?",
    "Answer": "C",
    "Explanation": "Using the formula for exponential decay, V = P(1 - r)^t, we find V = 20000(0.85)^3 ≈ $12,206.25.",
    "PictureURL": "",
    "OptionA": "$15,000",
    "OptionB": "$13,000",
    "OptionC": "$12,206.25",
    "OptionD": "$10,000",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Depreciation Calculation",
    "Item": 12,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the derivative of the function f(x) = e^x?",
    "Answer": "A",
    "Explanation": "The derivative of e^x is e^x itself, which is a unique property of the exponential function.",
    "PictureURL": "",
    "OptionA": "e^x",
    "OptionB": "x * e^(x-1)",
    "OptionC": "1",
    "OptionD": "ln(e)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Derivative of Exponential Functions",
    "Item": 13,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "If you invest $500 at an interest rate of 6% compounded quarterly, how much will you have after 3 years?",
    "Answer": "B",
    "Explanation": "Using the formula A = P(1 + r/n)^(nt), we find A = 500(1 + 0.06/4)^(4*3) ≈ $598.53.",
    "PictureURL": "",
    "OptionA": "$550",
    "OptionB": "$598.53",
    "OptionC": "$600",
    "OptionD": "$650",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Compound Interest Calculation",
    "Item": 14,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  },
  {
    "Question": "What is the growth factor of an investment that grows from $1000 to $1500 in 4 years?",
    "Answer": "C",
    "Explanation": "The growth factor can be calculated as final amount/initial amount = 1500/1000 = 1.5.",
    "PictureURL": "",
    "OptionA": "1.2",
    "OptionB": "1.3",
    "OptionC": "1.5",
    "OptionD": "1.4",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Exponential & Logarithmic Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Growth Factor Calculation",
    "Item": 15,
    "Type": "multiple choice",
    "Path": "math/exponential_logarithmic"
  }
]