Exponential equations solved with logarithms, and continuous compounding
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
Milo solves 4 · 3^x = 50 with logs on a math club card. To the nearest hundredth, what is x?
Noah solves 5 · 2^x = 140 with logs on a math club card. To the nearest hundredth, what is x?
Pia solves 6 · 1.5^x = 40 with logs on a math club card. To the nearest hundredth, what is x?
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?
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?
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?
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?
Ms. Ortiz's savings fund pays 4% compounded continuously. To the nearest tenth of a year, how long does Kira find it takes $500 to grow to $850?
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?
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?
