Applications of Exponential Functions (base e)
Interactive practice questions
The population ($P$P) of bacteria in a colony over time ($t$t) is given by $P=e^{0.1t}$P=e0.1t.
Which of the following shows the graph of the population of bacteria over time?
Under certain climatic conditions the proportion $P$P of the current blue-green algae population to the initial population satisfies the equation $P=e^{0.007t}$P=e0.007t, where $t$t is measured in days from when measurement began.
Solve for $t$t, the number of days it takes the initial number of algae to double to the nearest two decimal places.
The proportion $P$P of the initial mass of a carbon isotope in a dead tree trunk after $t$t years is given by $P=e^{-\frac{\ln2}{5500}t}$P=e−ln25500t.
The half life is the number of years it takes for the amount of isotope present to drop to half the original amount.
Solve for the half life of this particular isotope.
The proportion $Q$Q of radium remaining after $t$t years is given by $Q=e^{-kt}$Q=e−kt, where $k$k is a constant.