1) Kate invests \( \$2,300\) in a savings account that earns \(4.7%\) interest compounded continuously. How long, in years, will it take for the account to quadruple in value?
2) Neena’s parents decided to invest in Apple when she was born. They purchased \(400\) shares of stock in Apple to help pay for her college. When they originally invested, it was \( \$27\) per share. Since then, the stock went up an average of \(5\%\) per year. How many years before the account will cover one year of college if Neena goes to her parents’ alma mater that charges \( \$30,000\) per year?
3) Tim bought a Lamborghini for \( \$203,600\). It is expected to depreciate at a steady rate of \(13\%\) per year. How many years will it take to depreciate to \( \$26,000\)?
4) How many years (\(t\), to the nearest tenth, is the half- life of radioactive atoms if they decay according to the function \( A=A_{o} e\strut{^{\left(-0.027 \right)t}}\)?
5) A new type of bacteria has an exponential growth model for the population of \( P=\dfrac{500}{1+26.4e^{\large{-0.32t}}}\) where \(t\) represents the number of days since the bacteria culture began and \(P\) is the number of bacteria.
a) How many bacteria did the culture begin with initially?
b) To the nearest half day, when will the bacteria levels reach \(300\)?
Solution Bank
2) Neena’s parents decided to invest in Apple when she was born. They purchased \(400\) shares of stock in Apple to help pay for her college. When they originally invested, it was \( \$27\) per share. Since then, the stock went up an average of \(5\%\) per year. How many years before the account will cover one year of college if Neena goes to her parents’ alma mater that charges \( \$30,000\) per year?
3) Tim bought a Lamborghini for \( \$203,600\). It is expected to depreciate at a steady rate of \(13\%\) per year. How many years will it take to depreciate to \( \$26,000\)?
4) How many years (\(t\), to the nearest tenth, is the half- life of radioactive atoms if they decay according to the function \( A=A_{o} e\strut{^{\left(-0.027 \right)t}}\)?
5) A new type of bacteria has an exponential growth model for the population of \( P=\dfrac{500}{1+26.4e^{\large{-0.32t}}}\) where \(t\) represents the number of days since the bacteria culture began and \(P\) is the number of bacteria.
a) How many bacteria did the culture begin with initially?
b) To the nearest half day, when will the bacteria levels reach \(300\)?
Solution Bank