Exponential equations solved with logarithms, and continuous compounding

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   A yeast culture has 500 · 2^(t/3) cells after t hours. To the nearest hundredth of an hour, when does Noah find 3,500 cells?

   8.42
2. 2.

   A duckweed patch has 80 · 3^(t/5) leaves after t days. To the nearest hundredth of a day, when does Pia find 900 leaves?

   11.02
3. 3.

   A sample of iodine-131 has 1200 · (1/2)^(t/8) mg after t days. To the nearest hundredth of a day, when does Ren find 200 mg?

   20.68
4. 4.

   Ms. Hale's savings fund pays 6% a year compounded monthly. To the nearest tenth of a year, how long does Zee find it takes $2,000 to grow to $3,000?

   6.8
5. 5.

   Mr. Dunn's savings fund pays 4% a year compounded quarterly. To the nearest tenth of a year, how long does Bo find it takes $5,000 to grow to $6,000?

   4.6
6. 6.

   Ms. Ortiz borrows $6,000 for a used car, paying nothing until the end, at 6% a year compounded monthly. To the nearest tenth of a year, when does Esme find the amount owed reaches $7,500?

   3.7
7. 7.

   Mr. Dunn compares $3,000 at 5% a year for 8 years: compounded continuously or simple interest. How much more does Jun find continuous compounding gives?

   $275.47
8. 8.

   Milo wants a savings fund, compounded continuously, to double in 10 years. As a percent to the nearest hundredth, what yearly rate does that need?

   6.93
9. 9.

   Noah wants a savings fund, compounded continuously, to triple in 25 years. As a percent to the nearest hundredth, what yearly rate does that need?

   4.39
10. 10.

    Pia wants a savings fund, compounded continuously, to grow by half in 8 years. As a percent to the nearest hundredth, what yearly rate does that need?

    5.07