Exponential equations solved with logarithms, and continuous compounding

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Jun solves 3^x = 20 on the class board by writing x = log 20 ÷ log 3. To the nearest hundredth, what is x?

   2.73
2. 2.

   Kira solves 2^x = 50 on the class board by writing x = log 50 ÷ log 2. To the nearest hundredth, what is x?

   5.64
3. 3.

   Milo solves 2 · 5^x = 40 in a math book. Which choice gives x as a logarithm?

   • x = log₅ 20
   • x = log₂₀ 5
   • x = log₅ 40
   • x = log 40
4. 4.

   Noah solves 3 · 2^x = 21 in a math book. Which choice gives x as a logarithm?

   • x = log₂ 7
   • x = log₂ 21
   • x = log₆ 21
   • x = log₇ 2
5. 5.

   Pia solves 4 · 3^x = 44 in a math book. Which choice gives x as a logarithm?

   • x = log₃ 11
   • x = log₁₂ 44
   • x = log₃ 44
   • x = log₁₁ 3

6. Read this first

   Use this

   Growth table, × 1.07 on each yearly arrow: row 0: $1; row 1: $1.07; row 2: $1.1449; the rows go on until $2.

7. 6.

   Mr. Dunn's savings fund earns 7% a year, compounded yearly, and Zee solves 1.07^t = 2. To the nearest tenth of a year, how long until the money doubles?

   10.2

8. Use this

   Growth table, × 1.04 on each yearly arrow: row 0: $1; row 1: $1.04; row 2: $1.0816; the rows go on until $2.

9. 7.

   Ms. Hale's savings fund earns 4% a year, compounded yearly, and Bo solves 1.04^t = 2. To the nearest tenth of a year, how long until the money doubles?

   17.7
10. 8.

    Mr. Dunn's savings fund pays 3% a year, compounded continuously. Using A = Pe^(rt), how much does Jun find $1,200 grows to in 5 years?

    $1,394.20
11. 9.

    Ms. Ortiz's savings fund pays 5% a year, compounded continuously. Using A = Pe^(rt), how much does Kira find $800 grows to in 4 years?

    $977.12
12. 10.

    Ms. Hale's savings fund pays 4% a year, compounded continuously. Using A = Pe^(rt), how much does Luz find $2,500 grows to in 6 years?

    $3,178.12