Exponential equations solved with logarithms, and continuous compounding

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Milo solves 4 · 3^x = 50 with logs on a math club card. To the nearest hundredth, what is x?

   2.3
2. 2.

   Noah solves 5 · 2^x = 140 with logs on a math club card. To the nearest hundredth, what is x?

   4.81
3. 3.

   Pia solves 6 · 1.5^x = 40 with logs on a math club card. To the nearest hundredth, what is x?

   4.68
4. 4.

   A lab sample has 60 mg of phosphorus-32, whose half-life is about 14 days. To the nearest tenth, how many days until Tala finds 25 mg left?

   17.7
5. 5.

   A lab sample has 40 mg of fluorine-18, whose half-life is about 110 minutes. To the nearest tenth, how many minutes until Zee finds 9 mg left?

   236.7
6. 6.

   Mr. Lee's used car is worth $9,000 and loses 12% of its value each year. To the nearest tenth of a year, when does Bo find it is worth $5,000?

   4.6
7. 7.

   A pond's duckweed covers 800 square meters and shrinks 15% each week. To the nearest tenth of a week, when does Esme find it covers 300 square meters?

   6
8. 8.

   A cup of cocoa is 50°F warmer than the room, and the gap shrinks 10% each minute. To the nearest tenth of a minute, when does Jun find the gap is 20°F?

   8.7
9. 9.

   Mr. Dunn's savings fund pays 5% compounded continuously. To the nearest tenth of a year, how long does Luz find it takes $2,000 to grow to $3,000?

   8.1
10. 10.

    Ms. Hale's savings fund pays 3% compounded continuously. To the nearest tenth of a year, how long does Milo find it takes $1,500 to grow to $2,100?

    11.2